help!! asap!
A bucket of paint has spilled on a tile floor. The paint flow can be expressed with the function p(t) = 5t, where t represents time in minutes and p represents how far the paint is spreading.

The flowing paint is creating a circular pattern on the tile. The area of the pattern can be expressed as A(p) = πp2.

Part A: Find the area of the circle of spilled paint as a function of time, or A[p(t)]. Show your work. (6 points)

Part B: How large is the area of spilled paint after 2 minutes? You may use 3.14 to approximate π in this problem. (4 points)

Answer:

10 cm

Step-by-step explanation:

If the length of a rectangle is equal to triple the width, the width of the rectangle is 10 cm if the perimeter is 80 centimeters.​

L = 3w

P = 80

Formula: a = l × w

8W = 80 cm

W = 80 / 8 = 10 cm

Therefore, the width of the rectangle is 10 centimeters.

The width of the rectangle is found to be 10 centimeters, obtained by solving the equation created based on the fact that the perimeter of a rectangle is 2(length + width) and the given data that length is thrice the width and perimeter is 80 cm.

To figure out the width of the rectangle, we first need to understand the relationship between the length and width, and how they relate to the perimeter. The length of the rectangle is triple the width. Let's define the width as 'w'. Therefore, the length would be '3w'.

The formula for the perimeter of a rectangle is 2(length + width).

Given that the perimeter is 80 centimeters, we can set up the equation 2(3w + w) = 80. Simplifying this gives 8w = 80. To find the width 'w', we divide both sides of the equation by 8, giving us w = 10 centimeters.

Therefore, the width of the rectangle is 10 centimeters.

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Answer:

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Step-by-step explanation:

We are given the graph with a rectangular figure WXYZ and we are to find the coordinates of its vertices W'X'Y'Z' after the transformation of 90° rotation.

We know that, the rule for 90° rotation of a point (x, y) gives (-y, x).

So,

W (-1, 4) ---> W' (-4, -1)

X (-1, 2)  ---> X' (-2, -1)

Y (2, 2)  ---> Y' (-2, 2)

Z (2, 4)  ---> Z' (-4, 2)

Answer

W'

✔(-4,1)

X'

✔ (-2, -1)

Y'

✔ (-2, 2)

✔Z'(–4, 2)

Step-by-step explanation:

Answer:

14 ft/sec

so 14 feet in one second.

Hope this helps you :)

Good Luck :)))

Answer:

14 feet per second

Step-by-step explanation:

If a ball travels on a straight surface at 20 ft/sec and begins to decrease at 6 ft/sec, it will travel 14 feet per second.

Answer:

- 90

Step-by-step explanation:

These are the terms of an arithmetic sequence with n th term

[tex]a_{n}[/tex] = a + (n - 1)d

where a is the first term and d the common difference

d = 6 - 9 = 3 - 6 = - 3 and a = 9, hence

[tex]a_{34}[/tex] = 9 - 3 × 33 = 9 - 99 = - 90

The [tex]a_{34}[/tex] is -90 in the given sequence.

The given sequence is 9,6,3,......

We are asked to find the [tex]34^{th}[/tex] term in the sequence which is denoted by  [tex]a_{34}[/tex].

We first need to know what type of sequence is given in the question.

A sequence where the difference between the consecutive terms is always the same.

The formula used to find the value of the required term is given by:

[tex]a_n = a + (n-1)d[/tex]

Where a = first term, n = the term value and d = common difference.

The given sequence is 9,6,3,.....

We see that the given sequence is an arithmetic sequence.

6 - 9 = -3 and 3 - 6 = -3

so,

d = -3.

Here a = 9.

And we need to find the value in the sequence at n = 34.

substituting a,d, and n values in  [tex]a_n = a + (n-1)d[/tex].

We get,

[tex]a_{34} = 9 + ( 34 - 1 ) (-3)\\a_{34} = 9 + 33(-3)\\a_{34} = 9 - 99\\a_{34} = -90[/tex]

Thus, the [tex]a_{34}[/tex] is -90 in the given sequence.

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Answer:

The integers are -5 , -6 ⇒ answer C

Step-by-step explanation:

* Lets explain the meaning of consecutive numbers

- Consecutive numbers are numbers that follow each other in order.

-  They have a difference of 1 between every two numbers

- Consider that the smaller of two consecutive integer is n, then the

  larger one will be n + 1

* In the problem

∵ The larger of the two consecutive integers is 7 greater than twice

  the smaller

- That means the larger one is 7 plus twice the smaller

∵ The smaller one is n

∵ The larger one is n + 1

∴ n + 1 = 2(n) + 7

∴ n + 1 = 2n + 7

- Subtract n from both sides

∴ 1 = n + 7

- Subtract 7 from both sides

∴ -6 = n

∴ The smaller number is -6

∵ The greater number is n + 1

∴ The greater number = -6 + 1 = -5

* The integers are -6 , -5

Answer:

6x + 8 = 32

Step-by-step explanation:

Let the number be= x

So 6 times a certain number is added to 8 which gives the answer 32.

6( x ) + 8 = 32

6x + 8 = 32

Hence this is the equational form.

On further solving we get,

6x = 32 - 8

6x = 24

x = 24 / 6

x = 4....

Answer:

The required equation is 6x+8=32

Step-by-step explanation:

Consider the provided information.

6 times a certain number is added to 8, the result is 32

Let the number is represents by x.

6 times of a number can be written as: 6x

Add 8 to the above expression.

6x+8

The expression is equal to 32.

Thus, the required equation is 6x+8=32

Answer:

[tex]y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})[/tex] point-slope form

[tex]13x+3y=11[/tex] (standard form)

Let me know if you prefer another form.

Step-by-step explanation:

The slope of a line can be found using [tex]\frac{y_2-y_1}{x_2-x_1}[/tex] provided you are given two points on the line.

We are.

Now you can use that formula.  But I really love to just line up the points vertically then subtract them vertically then put 2nd difference over 1st difference.

 (4/5  ,  1/5)

-( 1/2  ,  3/2)

-----------------

3/10          -13/10

2nd/1st = [tex]\frac{\frac{-13}{10}}{\frac{3}{10}}=\frac{-13}{3}[/tex] is our slope.

So the following is point-slope form for a linear equaiton:

[tex]y-y_1=m(x-x_1) \text{ where } m \text{ is slope and } (x_1,y_1) \text{ is a point on the line }[/tex]    

Plug in a point [tex](x_1,y_1)=(\frac{1}{2},\frac{3}{2}) \text{ and } m=\frac{-13}{3}[/tex].

This gives:

[tex]y-\frac{3}{2}=\frac{-13}{3}(x-\frac{1}{2})[/tex]

I'm going to distribute:

[tex]y-\frac{3}{2}=\frac{-13}{3}x-\frac{-13}{6}[/tex]

Now I don't like these fractions so I'm going to multiply both sides by the least common multiply of 2,3, and 6 which is 6:

[tex]6y-9=-26x+13[/tex]

Add 26x on both sides:

[tex]26x+6y-9=13[/tex]

Add 9 on both sides:

[tex]26x+6y=22[/tex] This is actually standard form of a line.

It can be simplified though.

Divide both sides by 2:

[tex]13x+3y=11[/tex] (standard form)

Answer:

[tex]\large\boxed{y=-\dfrac{13}{3}x+\dfrac{11}{3}}-\bold{slope\ intercept\ form}\\\boxed{13x+3y=11}-\bold{standard\ form}[/tex]

Step-by-step explanation:

The slope-intercept form of an equation of a line:

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

m - slope

b - y-intercept

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

We have two points

[tex]\left(\dfrac{4}{5},\ \dfrac{1}{5}\right),\ \left(\dfrac{1}{2},\ \dfrac{3}{2}\right)[/tex]

Convert fractions to the decimals

(divide the numerator by the denominator) :

[tex]\dfrac{4}{5}=0.8,\ \dfrac{1}{5}=0.2,\ \dfrac{1}{2}=0.5,\ \dfrac{3}{2}=1.5[/tex]

[tex]\left(\dfrac{4}{5},\ \dfrac{1}{5}\right)=(0.8,\ 0.2)\\\\\left(\dfrac{1}{2},\ \dfrac{3}{2}\right)=(0.5,\ 1.5)[/tex]

Calculate the slope:

[tex]m=\dfrac{1.5-0.2}{0.5-0.8}=\dfrac{1.3}{-0.3}=-\dfrac{13}{3}[/tex]

Put the value of slope and the coordinates of the first point to the equation of a line:

[tex]0.2=-\dfrac{13}{3}(0.8)+b[/tex]      multiply both sides by 3

[tex]0.6=(-13)(0.8)+3b[/tex]

[tex]0.6=-10.4+3b[/tex]           add 10.4 to both sides

[tex]11=3b[/tex]           divide both sides by 3

[tex]\dfrac{11}{3}=b\to b=\dfrac{11}{3}[/tex]

Finally:

[tex]y=-\dfrac{13}{3}x+\dfrac{11}{3}[/tex] - slope-intercept form

Convert to the standard form (Ax + By = C):

[tex]y=-\dfrac{13}{3}x+\dfrac{11}{3}[/tex]      multiply both sides by 3

[tex]3y=-13x+11[/tex]          add 13x to both sides

[tex]13x+3y=11[/tex] - standard form

Answer:

Range is y > 0

Step-by-step explanation:

We need to find the range of y = e^4x

The range is defined as a set of values of dependent variable for which the function is defined.

The exponential function of form c. n^x + k has range f(x) > k

in the given function y = e^4x ,k =0

so Range is y > 0

In the system of equations, x represents the number of tickets of Level 1 seats while y represents the number of tickets of Level 2 seats.

Given to us,

system of equations,

Equation 1, 150x + 250y = 125,000,

Equation 2,  x + y = 50,000,

Total number of seats = 50,000 seats,

Total number of sales = $125,000,

Level 1 tickets price = $150,

Level 2 tickets price = $250,

Let us assume, Number of tickets of Level 1 is [tex]\bold x[/tex], and, Number of tickets of Level 2 is [tex]\bold y[/tex],

Total sales = (Number of tickets of Level 1 x Level 1 tickets price ) + (Number of  tickets of Level 2 x Level 2 tickets price )

125,000 = ([tex]\bold x[/tex] x 150) + ([tex]\bold y[/tex] x 250)

125,000 = 150x + 250y

Now,

Total number of seats = Number of tickets of Level 1 + Number of tickets of Level 2

50,000 = x + y

Therefore, In the system of equations, x represents the number of tickets of Level 1 seats while y represents the number of tickets of Level 2 seats.

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The variables x and y represent the number of Level 1 and Level 2 tickets sold, respectively. These variables show how many of each type of ticket were sold at their respective prices ($150 and $250) to achieve a total sale of $125,000.

The problem presents a linear system of equations that models the pricing of tickets sold at a concert.

The equations are:

In this system:

Therefore, these equations together show the total number of tickets sold and the total revenue from these tickets.

Answer:

The radius is [tex]\frac{\sqrt{74}}{2}[/tex].

The center is (5/2 , 9/2).

Step-by-step explanation:

The radius is half the diameter.  We aren't given the length of the diameter but we are given endpoints to one of them.

So let's find the length of that diameter using the distance formula.

The distance formula is

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

I just do big x minus small x or big y minus small y.

Anyways the points are (-1,7) and (6,2).

The x distance is 6-(-1)=7.

The y distance is 7-2=5.

So we have this using the distance formula so far:

[tex]d=\sqrt{(6-(-1))^2{(7-2)^2}[/tex]

[tex]d=\sqrt{7^2+5^2}[/tex]

[tex]d=\sqrt{49+25}[/tex]

[tex]d=\sqrt{74}[/tex]

So the radius is half that much because that was the distance between the endpoints of a diameter.

So the radius is [tex]\frac{\sqrt{74}}{2}[/tex].

Now the center of a circle will lie on the midpoint of a diameter, any given diameter.

We have the endpoints of one, so we just need to use midpoint formula.

Midpoint formula says the midpoint is (average of x, average y).

Midpoint formula: [tex](\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex].

So average of x's is (-1+6)/2=5/2.

The average of y's is (7+2)/2=9/2.

So the midpoint of the diameter or the center of the circle is at (5/2 , 9/2).

Answer:

slope = - [tex]\frac{1}{2}[/tex]

Step-by-step explanation:

The equation of a line in point- slope form is

y - b = m(x - a)

where m is the slope and (a, b) a point on the line

y - 3 = - [tex]\frac{1}{2}[/tex](x - 2) ← is in point- slope form

with slope m = - [tex]\frac{1}{2}[/tex]

Answer:

y= -5x+12

Step-by-step explanation:

slope int form ; y=mx+b

that is the only option in that form.

Answer:

the equation is y = 5x + 12

Step-by-step explanation:

The equation of line is 10x - 2y=-2

Write this equation in slope intercept form of line y = mx + b

[tex]10x-2y=-2\\\\2y=10x+2\\\\y=5x+1[/tex]

Therefore, the slope of the line is m = 5

Now, we know that parallel lines have same slope.

Hence, slope of the required line is also 5.

Thus, the equation of line is in the form y = 5x + b

Now, use the point (0,12) to find b

12= 5(0) + b

b = 12

Hence, the equation is y = 5x + 12

Answer:

American Bison

Step-by-step explanation:

First find out how many feet the bison runs in an hour.

To find that out you have to multiply 3520 by 60 minutes because there are 60 minutes in an hour.

So 3520*60 = 211,200 feet

Then you have to convert 211,200 feet into miles and since there are 5,280 feet in an a mile you have to divide.

So 211,200 divided by 5,280 = 40

So the American Bison runs 40 miles per hour which is faster than the White Tailed Deer who only runs 30 miles per hour.

So the answer is the American Bison.

Answer:

[tex]\large\boxed{\dfrac{5}{11}}[/tex]

Step-by-step explanation:

[tex]\text{Use}\ P(A\ \cup\ B)=P(A)+P(B)-P(A\ \cap\ B).\\\\\text{We have:}\\\\P(A)=\dfrac{4}{11},\ P(B)=\dfrac{3}{11},\ P(A\ \cup\ B)=\dfrac{2}{11}.\\\\\text{Substitute:}\\\\\dfrac{2}{11}=\dfrac{4}{11}+\dfrac{3}{11}-P(A\ \cap\ B)\\\\\dfrac{2}{11}=\dfrac{7}{11}-P(A\ \cap\ B)\qquad\text{subtract}\ \dfrac{7}{11}\ \text{from both sides}\\\\-\dfrac{5}{11}=-P(A\ \cap\ B)\qquad\text{change the signs}\\\\P(A\ \cap\ B)=\dfrac{5}{11}[/tex]

[tex]\huge{\boxed{25}}[/tex]

The radius is the distance from the center of the circle to its edge.

The diameter is the distance from one point on the edge to the opposite point on the edge, so it is twice as much as the radius.

This means we just need to multiply the radius by two to get the diameter. [tex]2r=d[/tex]

[tex]2(12.5)=d[/tex]

[tex]\boxed{25}=d[/tex]

Write it out as an equation:

3 < 1/3P

Rewrite so P is on the left side:

1/3P >3

Multiply each side by 3:

1/3P x 3 > 3 x 3

Simplify:

P > 9

[tex]g(f(x))=3x+2+5=3x+7[/tex]

Answer:

See below in bold.

Step-by-step explanation:

(g + h)(x) = 4x - 4 + x - 5

= 5x - 9.

(g - h)(x) = 4x - 4 - (x - 5)  ( Note we put the x - 5 in parentheses)

= 4x - 4 - x + 5

=  3x + 1.

(g.h)(x) = (4x - 4)(x - 5)

so (g.h)(1) = (4(1) - 4)(1 - 5)

= 0 * -4

= 0.

The product of the functions will be (g·h)(x) = 4x² – 24x + 20. At x = 1, the product of the functions is zero.

A statement, principle, or policy that creates the link between two variables is known as a function.

The functions are given below.

g(x) = 4x – 4

h(x) = x – 5

Then the sum of the functions will be

(g + h)(x) = (4x – 4) + (x – 5)

(g + h)(x) = 4x – 4 + x – 5

(g + h)(x) = 5x – 9

Then the difference in the functions will be

(g – h)(x) = (4x – 4) – (x – 5)

(g – h)(x) = 4x – 4 – x + 5

(g – h)(x) = 3x + 1

Then the product of the functions will be

(g·h)(x) = (4x – 4)(x – 5)

(g·h)(x) = 4x² – 4x – 20x + 20

(g·h)(x) = 4x² – 24x + 20

At x = 1, then we have

(g·h)(x) = 4(1)² – 24(1) + 20

(g·h)(x) = 4 - 24 + 20

(g·h)(x) = 0

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Answer:

The area of the field = 19966.21 units²

Step-by-step explanation:

* Lets explain how to find area of a triangle by trigonometry rule

- In any triangle if you have the lengths of two sides and the measure

 of the including angle between these two sides, then the area of the

 triangle is A = [tex]\frac{1}{2}s_{1}s_{2}sin\alpha[/tex] , wher α is the

 including angle between them

* Lets solve the problem

∵ The field is shaped triangle

∵ The lengths of two sides of the field are 218.5 and 213.3

∴ s1 = 218.5

∴ s2 = 213.3

∵ The measure of the angle between the two sides is 58.96°

∴ α = 58.96°

- Lets find the area using the rule of trigonometry

∴ [tex]A=\frac{1}{2}(218.5)(213.3)sin(58.96)=19966.21[/tex]

∴ The area of the field = 19966.21 units²

Answer:

The correct answer is first option

x = 12, y = 10

Step-by-step explanation:

From the figure we can see that a triangle ADC, and EB is parallel to side DC.

To find the value pf x

From the given figure we get,

<ABC = <BCD  [ corresponding angles are equal]

3x + 9 = 4x - 3

4x - 3x = 9 + 3

x = 12

To find the value of y

<ABE and <EBC are linear pairs.

Therefore, <ABE + <EBC = 180

(3x + 9)  + (14y - 5) = 180

(3 * 12 + 9) + 14y - 5 = 180

45 + 14y - 5 = 180

14y = 180 -40

14y = 140

y = 140/14 = 10

y = 10

Therefore x = 12 and y = 10

The correct answer is first option

Answer:

B and C

Step-by-step explanation:

There are 3 conditions for the difference of squares.

The correct answer is B and C

Final answer:

Binomials that are a difference of squares have the form a² - b² and can be factored into (a + b)(a - b), where both terms are perfect squares. Examples include x² - 9 and 4y² - 25.

Explanation:

To determine which binomials are a difference of squares, we look for expressions in the form of a2 - b2. A difference of squares can be factored into (a + b)(a - b), where a and b are any expressions. It is essential that both terms be perfect squares and that they are subtracted from one another.

For example, x2 - 9 is a difference of squares as it can be factored into (x + 3)(x - 3), where both x2 and 9 are perfect squares. Another example could be 4y2 - 25, which factors to (2y + 5)(2y - 5). Keep in mind that if the sign is not subtraction, or if either term is not a perfect square, the binomial does not represent a difference of squares. The correct choice of examples, factoring process, and the nature of perfect squares are essential to identify differences of squares accurately.

Answer:

C; The left end goes up; the right end goes down

Step-by-step explanation:

If you expand the function, you end up with a polynomial with a negative coefficient and it has an odd power. According to polynomial behaviors of a function that is odd negative, the graph will rise to the left (y → ∞ and x → -∞) and falls to the right (y → -∞ and x → ∞).

ANSWER

C. The left end goes up; the right end goes down.

EXPLANATION

The given function is

[tex]f(x) = - 2( {x - 2)}^{5} [/tex]

We analyze the end behavior of this function using the leading term.

The leading term of this function is:

[tex] - 2 {x}^{5} [/tex]

Since the degree(5) is odd and the leading coefficient (-2) is negative, the graph rises on the left and falls on the right.

In other words, the left end of the graph goes up and the right end goes down.

The correct option is C.

Answer: 123.5 in^2

Step-by-step explanation: The formula for the area of a trapezoid is a+b/2 x h. In other words, base 1 plus base 2 divided by 2, and multiplied by the height. Plug in the numbers. The equation is:

6+7/2 x 19 = 123.5.

Since you are finding the area, the answer would be in inches squared. The answer is 123.5 in^2.

The answer is A.75°

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

75+35+x = 180.

x = 180-75-35

x = 75

A triangle is a three-sided polygon, which has three vertices. The three sides are connected with each other end to end at a point, which forms the angles of the triangle.

The sum of all three angles of the triangle is equal to 180 degrees.

The angles of a triangle always add up to 1800 degrees because one exterior angle of the triangle is equal to the sum of the other two angles in the triangle. When all the angles are added up, the sum obtained should be 180 degrees.

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Answer:

[tex]log_{7} \frac{7}{x^{2} }[/tex]

Step-by-step explanation:

We need to write [tex]1 - 2log_{7}x[/tex] as a single logarithm.

We know that

[tex]log_{7}7 = 1[/tex]

Therefore we have:

[tex]log_{7}7 - 2log_{7}x[/tex]

→ [tex]log_{7}7 - log_{7}x^{2}[/tex]

→ [tex]log_{7} \frac{7}{x^{2} }[/tex]

The solution is: [tex]log_{7} \frac{7}{x^{2} }[/tex]

Answer:

The correct option is C

Step-by-step explanation:

81x²+72x+16

We have to break the middle term:

If we multiply 81 by 16 we get 1296:

The same answer we get when we multiply 36 by 36:

36*36=1296

And if we add 36+36 then we get the middle term which is 72.

So,

=81x²+72x+16

=81x²+36x+36x+16

=9x(9x+4)+4(9x+4)

=(9x+4)(9x+4)

Thus the correct option is C ....

Answer:

don´t exist

Step-by-step explanation:

The slant asymptote only exist under two condition:

1) Don't exist horizontal asymptote  

2) If the degree of the denominator is n, the degree of the numerator should be n+1

In this case, the degree of the numerator is n+2, for that the slant asymptote don´t exist

Answer:

Up down and side to side on the graph

Step-by-step explanation:

If a is 1, since it is positive the parabola moves up. If a is -1, since it is negative the parabola moves down. (not sure about side to side because I can't back that one up but I'm 100% sure about up and down)

When a is between 0 and 1, the parabola gets wider.

A parabola is a mathematical curve that is defined by a point and a line. The point is known as the focus, and the line is called the directrix. The parabola has the property that all points on it are equidistant from the focus and the directrix.

Here,

When a is negative, the parabola flips 180°.

When |a| is less than 1, the parabola opens wider.

When |a| is greater than 1, the parabola opens more narrow.

When a is between 0 and 1, the parabola gets wider, when it is greater than 1, it gets narrower, and when it is less than 0 it is reflected across the x-axis.

Therefore, when a is between 0 and 1, the parabola gets wider.

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