Answer with steps!... Thanks

Answer:

Step-by-step explanation:

Since the area pollute sis assumed to be a circle, we will be using the formula for calculating the area of a circle to solve the problem.

Area of a circle A = πr²

r is the radius of the circle

The rate at which the area is increasing is expressed as dA/dt. According to chain rule, dA/dt = dA/dr*dr/dt where;

dr/dt is the rate at which the area is increasing.

If dA/dr = 2πr (by mere differentiation)

dA/dt = 2πr * dr/dt

Given dr/dt = 3ft/sec and r = 30feet

dA/dt = 2π(30) * 3

dA/dt = 180π ft/sec

Hence, the area is increasing at the rate of 180π ft/sec

Answer:

The surface area of the pyramid is 80.9 cm²

Step-by-step explanation:

The side length, s of the cube is given as 5 cm

Therefore, the largest pyramid that can fit into the cube will have a base side length, s = The side length of the cube = 5 cm

The height, h of the largest pyramid = The height of the cube = 5 cm.

The surface area of a pyramid =  Area of base, A + 1/2 × Perimeter of base, P × Slant height, S

The slant height of the pyramid = √(h² + (s/2)²) = √(5² + (5/2)²) = (5/2)×√5

The perimeter of the base = 4×5 = 20 cm

The area of the base = 5×5 = 25 cm²

The surface area of a pyramid = 25 + 1/2×20×(5/2)×√5 = 80.9 cm².

The surface area of a pyramid =  80.9 cm².

Answer:

(a) y =  3x + 2; (b) (0,2); (c) y = 3x - 8; (d) (2,-2)

(e) Area of ∆ABC = 30; (f) Area of ABCD = 40

Step-by-step explanation:

(a) Equation of AD

(i) Slope of AB

m₁ = (y₂ - y₁)/(x₂ - x₁) = (6 - 8)/(8 - 2)= -2/6 = -⅓

(ii) Slope of AD

m₂ = 3

(ii) y-intercept

y = 3x + b

8 = 3(2) + b= 6 + b

b = 2

The equation of AD is y = 3x + 2.

(b) Coordinates of D

The coordinates of D are (0,2).

(c) Equation of perpendicular bisector of AB

(i) Mid-points of AB

x = ½(x₂ + x₁) = ½(8 + 2) = ½(14) = 5

y = ½(y₂ + y₁) = ½(6 + 8) = ½(14) = 7

The coordinates of the mid-point are (5,7).

Slope = 3

y = mx + b

7 = 3(5) + b = 15 + b

b = 7 - 15 = -8

The equation of the perpendicular bisector is y = 3x - 8.

(d) Coordinates of C

C is at the intersection of BC and the perpendicular bisector of AD.

 y = 3x -    8

3y = 4x - 14

3y = 9x - 24

 0 = 5x - 10

5x = 10

 x =   2

 y = 3(2) - 8  = 6 - 8 = -2

The coordinates of C are (2,-2).

(e) Area of ∆ABC

A = ½bh = ½ × 10 × 6 = 30

(f) Area of ABCD

Area of ∆ACD = ½bh = ½ × 10 × 2 = 10

Area of ABCD = ∆ACD + ∆ABC =10 + 30 = 40

Answer:

2x -5

Step-by-step explanation:

-3 + 2(x - 1)

Distribute

-3 +2x -2

Combine like terms

2x -5

Answer:

5x -2

Step-by-step explanation:

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

Explanation:

The radius of the circle is r, which doubles to 2r to get the diameter. The diameter of the circle is also the diagonal of the square. Consequently, this means we have two right triangles in which they have the same hypotenuse of 2r.

Let x be the side length of the square. Use the pythagorean theorem to isolate x

a^2 + b^2 = c^2

x^2 + x^2 = (2r)^2

2x^2 = 4r^2

x^2 = 2r^2 ... divide both sides by 2

x = sqrt(2r^2) ... apply the square root to both sides; keep in mind that x > 0

x = sqrt(r^2*2)

x = sqrt(r^2)*sqrt(2)

x = r*sqrt(2)

The side length of the square is r*sqrt(2)

Therefore, the area of the square is

Area = (side)*(side)

Area = ( r*sqrt(2) )*( r*sqrt(2) )

Area = r*r * sqrt(2)*sqrt(2)

Area = r^2 * sqrt(2*2)

Area = r^2 * sqrt(4)

Area = r^2 * 2

Area = 2r^2

Step-by-step explanation:

a drop in temperature means the temperature will decrease.

That decrease is represented with a negative integer which should be added to the previous temperature.

Answer:

The required fraction is 3/5

Answer:  3/5

Step-by-Step Explanation:

Let x represent the denominator of the fraction, then we have [tex]\dfrac{x-2}{x}[/tex]

Now add 3 to the numerator and 5 to the denominator and set it equal to 3/5:

[tex]\dfrac{(x-2)+3}{(x)+5}=\dfrac{3}{5}\\\\\\\text{Simplify:}\\\dfrac{x+1}{x+5}=\dfrac{3}{5}\\\\\\\text{Cross Multiply and solve for x:}\\5(x+1)=3(x+5)\\5x+5=3x+15\\2x=10\\x=5[/tex]

Substitute x = 5 into the original fraction:

[tex]\dfrac{(5)-2}{(5)}\quad =\large\boxed{\dfrac{3}{5}}[/tex]

Answer:

d:48:(48+36)

Step-by-step explanation:

cause the length PT corresponds to PQ so the value of PT which is 48 corresponds with the value of PQ which is 48+36 I guess

Option d 48:(48+36) is the correct option.

Given that:

Statements that Nora wrote are:

Statement Reason

1. Segment ST is parallel to segment RQ Given

2. Angle QRS is congruent to angle TSP Corresponding angles formed by parallel lines and their transversal are congruent

3. Angle SPT is congruent to angle RPQ Reflexive property of angles

4. Triangle SPT is similar to triangle RPQ Angle-Angle Similarity Postulate

5. 60: (60+x) = ?

It is the property that a line intersecting and cutting a triangle which is parallel to a side of that triangle has those cuts with proportionate measures.

In the given figure, the above fact is shown symbolically as:

[tex]\dfrac{PS}{PR} = \dfrac{PT}{PQ}\\[/tex]

Thus we have :

[tex]\dfrac{60}{60+x} = \dfrac{48}{48+36}\\[/tex]

Thus Option d  48:(48+36) is the correct option.

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Answer:

They donated 7/10 of their profits. This cannot be simplified any further.

mark me BRAINLIEST

Tysmm!!

Answer:

Step-by-step explanation:

2/10 and 1/10 are easily addable fractions so all you have to do is add the numerator to get, 3/10. After that you need to convert 2/5 into tenths so that you can continue to add it correctly. If you multiply the numerator and the denominator of 2/5 to convert it, you will get 4/10 to add.

Answer: 7/10

Answer:

A

Step-by-step explanation:

If the post of the fence is 10 feet long. And we know that 3(1/3) of the fence is underground. We just need subtract 3(1/3) from 10.

10-3=7

7-(1/3)=6(2/3)

Answer:

-58.41509433

Step-by-step explanation:

0.4+8(5-0.8*5/8)-5/(2.5)=34.4

[0.4+8(5-4/8)-(2)]=

[0.4+8(40-4)/8)-2=34.4 ( nominator)

15-(8.9-2.6/(2/3))*34*2/5 =-53

15-(8.9-3.9)*68/5

15-5*68/5=

15-68=-53 ( denominator)

(34.4/-53) *90

-58.41509433

Answer:

[tex]\frac{n(n-3)}{2}[/tex]

Step-by-step explanation:

Polygon Diagonals are a pattern that follows a specific rule which can be used through a specific formula. Remember that Math focuses on patterns to create equations that help to study them, and this case is not an exception.

The equation for polygon diagonals is

[tex]\frac{n(n-3)}{2}[/tex]

Where [tex]n[/tex] refers to the number of sides of the polygon.

You see, a diagonal is defined as the union between two non-consecutive vertices. For a convex n-sided polygon, there are going to be n vertices, and we can draw [tex]n-3[/tex] from each vertex, then we multiply this by [tex]n[/tex], because that's the total number of sides.

In the end, we divide by 2, because with the method described, we will have double number of diagonals.

Answer:

mRT = 4√13 ≈ 14.42

mST = 10√2 ≈ 14.14

Step-by-step explanation:

Pythagorean Theorem: a² + b² = c²

Since we have right triangles, in order to find the missing side, we use Pythagorean Theorem:

mTR:

12² + 8² = c²

144 + 64 = c²

c² = 208

c = √208 = 4√13

mST:

15² = 5² + b²

225 - 25 = b²

b² = 200

b = √200 = 10√2

To get your decimals, simply evaluate the square roots:

4√13 = 14.4222

10√2 = 14.1421

Answer:

6. 56.3 degrees.

7. 70.5 degrees.

Step-by-step explanation:

6. We are given the opposite and adjacent side lengths, so we can use tangent to solve this (TOA = Tangent; Opposite over Adjacent).

tan(R) = 12 / 8

tan(R) = 3 / 2

R = cotan(3/2)

R = 56.309932474020213

So, the measure of angle R is about 56.3 degrees.

7. We are given the adjacent and the hypotenuse, so we can use cosine to solve this (CAH = Cosine; Adjacent over Hypotenuse).

cos(R) = 5 / 15

cos(R) = 1/3

R = sec(1/3)

R = 70.528779365509

So, the measure of angle R is about 70.5 degrees.

Hope this helps!

Answer:

(-1, -2)

Step-by-step explanation:

Look up each point in the choices on the graph. If it is on the line or in the shaded area it is a solution.

Answer: (-1, -2)

Answer:

First & Last

Step-by-step explanation:

See what is in the red portion(Shaded or line), that is what can work to the inequality.

(-1, -2) -- In the red(works)

(-1, 2) -- Out of the red(Nope)

(0, 5.2) -- Out of the red(Nope)

(-2, -1) -- In the red(works)

Answer:

(5^2)(11^2)

Step-by-step explanation:

Taking all the factors in the left hand side of the factor tree, we have

5,5,11,11

5 twice

5^2=25

11 twice

11^2=121

The factor of 3,025=(5^2)(11^2)

Alternatively

3025÷5=605

605÷5=121

121÷11=11

11÷11=1

We have prime number 5 as divider twice and prime number 11 as a divider twice

Therefore,

5^2*11^2=3,025

Check

(5^2)(11^2)

=(25)(121)

=3,025

Answer:

c

Step-by-step explanation:

Answer: 445 triangles can be form with 15 dots of a circle (I hope good luck)

Step-by-step explanation:

Answer:

455

Step-by-step explanation:

There are 15 points on a circle.

We need three points to form a triangle

Therefore the number of triangles = 15 choose 3 ​= 15!/(3!x12!)​ = (15x14x13)/(3x2x1) = 5x7x13 = 455

Hence the number of triangles formed is 455

Answer:

d

Step-by-step explanation:

Answer:

Interquartile Range: 21.549999999999997 = 21.55

Step-by-step explanation:

Answer:

Step-by-step explanation:

The formula for the volume of a sphere is

[tex]V=\frac{4}{3}\pi r^3[/tex] In order to use this formula we have to have a value for the radius and right now we don't. But we can find it indirectly by using the circumference formula. The circumference formula is

[tex]C=2\pi r[/tex] If the circumference is 20π, then we will fill that in for "C" and solve for r:

20π = 2πr and if you divide both sides by 2π, you'll get that r = 10. Now we have a radius.

Using that in the volume formula:

[tex]V=\frac{4}{3}\pi (10)^3[/tex] and then simplifying a bit:

[tex]V=\frac{4}{3}\pi (1000)[/tex] and

[tex]V=\frac{4000\pi}{3}[/tex] which divides to give you

[tex]V=1333.33\pi[/tex], third choice down.

Answer:

-5-2c

Step-by-step explanation:

The additive inverse of a term must be the opposite of it.

●-(5+2c)

●-5-2c

Answer:

Step-by-step explanation:

The additive inverse is just the opposite of the binomial in terms of the signs. The additive inverse of 5 + 2C is -(5 + 2C) which is, without parenthesis,        -5 - 2C.

The answer to this question will depend on the function f itself. Basically you will find the height in meters above the ground of the bird when it jumped when the time t=0s. This is substsitute every t in the function for a value of zero and that way you will get the bird's height at the time it jumped. If you were given a graph for this function, you can find the y-intercept of the graph and that will be the answer as well. The question could be written like this:

A baby bird jumps from a tree branch and flutters to the ground. The function "[tex]f(t)-4.9t^{2}+25[/tex]" models the bird's height (in meters) above the ground as a function of time (in seconds) after jumping. What is bird's height above the ground when it jumped.

Answer:

25m

Step-by-step explanation:

Once your function is given, you can substitute t=0 since 0s is the time measured at the moment the bird jumped. So our function will be:

[tex]f(0)=-4.9(0)^2+25[/tex]

[tex]f(0)=25m[/tex]

So the height of the bird above the ground when it jumped is 25m in this particular function.

Answer:

It is (0,12) on the graph , if you are doing it on Khan Academy.

Step-by-step explanation:

Just try it . se what happens. :))

Answer:

see derivation below

Step-by-step explanation:

Show that:

( sec(t) - cosec(t) ) ( 1 + tan(t) + cot(t) ) =

sec(t) tan(t) - cosec(t) cot(t)

Some trigonometric definitions used:

tan(t) = sin(t)/cos(t)

cot(t) = cos(t)/sin(t)

sec(t) = 1/cos(t)

csc(t) = 1/sin(t)

some trigonometric identities used:

sin^2(t) + cos^2(t) = 1 ......................(1)

rewrite left-hand side in terms of sine and cosine

(1/cos(t) - 1/sin(t) ) ( 1 + sin(t)/cos(t) + cos(t)/sin(t) )

Simplify using common denominator sin(t)cos(t)

= ( (sin(t) - cos(t))/(sin(t)*cos(t)) ) * ( ( sin(t)cos(t) + sin^2(t) + cos^2(t)) / ( sin(t)cos(t) ) )

= ( sin(t) -cos(t) ) * (1 + sin(t)cos(t) ) / ( sin^2(t) cos^2(t) )   ...... using (1)

Expand by multiplication

= ( sin(t) -cos(t) + sin^2(t)cos(t) - sin(t)cos^2(t) ) / ( sin^2(t) cos^2(t) )

Rearrange by factoring out sin(t) and cos(t) in numerator

= ( sin(t) (1-cos^2(t) - cos(t)(1-sin^2(t) )  / ( sin^2(t) cos^2(t) )

= ( sin^3(t) - cos^3(t) ) /( sin^2(t) cos^2(t) )   .........................using (1)

Cancel common factors

= sin(t)/(cos^2(t)) - cos(t)/(sin^2(t))

Rewrite using trigonometric definitions

= sec(t)tan(t) - csc(t)cot(t)   as in Right-Hand Side

Answer:

175 balls

Step-by-step explanation:

If 12.5 percent of the balls had defects, then [tex]100-12.5=87.5[/tex]% of balls didn't have defects.

We can find 87.5 percent of 200 by converting 87.5 to a decimal.

87.5% as a decimal is 0.875.

Now we multiply this decimal by 200.

[tex]200\cdot0.875 = 175[/tex]

So, 175 balls didn't have defects.

Hope this helped!

Answer:

2 tickets left

Step-by-step explanation:

12✖️29=348

350-348=2

Answer:

If they play the maximum number of games, there will be two tickets left over.

Step-by-step explanation:

For this problem, I used long division.

350 divided by 12 comes out to be 29.

29 is the maximum number of games they could play.

29 times 12 is 348.

350 (the total number of tickets) minus 348 (number of tickets used) comes out to be two.

Hope this helps! Brainliest would really help me out :)

Answer:

Step-by-step explanation:

Multiply $9500 by .05 (5%) to get 475. That is 5% of $9500. Now subtract 475 from 9500 to get 9025. That is your answer!  

The value of car in month of January is, [tex]\$ 9975[/tex]

It is given that, At the end of any year a car is worth 5% less than what it was worth at the beginning of the year.

Since, car was worth $9 500 in December 2016.

Then, the value of car in month of January is, 105 % of value of car in moth of December.

So that, value of car in month of January is,

                                     [tex]=9500*\frac{105}{100}\\ \\=9500*1.05=9975[/tex]

The value of car in month of January is, [tex]\$ 9975[/tex]

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Answer:

(-3, -11)

i needed to put more characters so here

actually, it's very easy all u have to do is minus 3 from every number (not x) and you'll easly get -2 < x < 1

If u see this pls give me brainliest

The solution of the provided inequality equation is −2 < x < 1. Option D is the correct option, which says x is greater than number -2 but less than 1.

Inequality equation is the equation in which the two expressions are compared with greater than, less than or other inequality signs.

The inequality equation, which has to be solved for x is,

[tex]1 < x + 3 < 4[/tex]

In this equation, subtract 3 in each side of the equation,

[tex]1 -3 < x + 3-3 < 4-3[/tex]

Solve it further,

[tex]1 -3 < x + 3-3 < 4-3\\-2 < x < 1[/tex]

Thus, the solution of the provided inequality equation is −2 < x < 1. Option D is the correct option, which says x is greater than number -2 but less than 1.

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Answer:

this is som A sorry if you can't read it

Answer:

[tex]a_{n}[/tex] = [tex]\frac{1}{2}[/tex] n + 15

Step-by-step explanation:

The n th term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₆ = 18 and d = [tex]\frac{1}{2}[/tex] , then

a₁ + 5d = 18 , that is

a₁ + [tex]\frac{5}{2}[/tex] = 18 ( subtract [tex]\frac{5}{2}[/tex] from both sides )

a₁ = [tex]\frac{31}{2}[/tex]

Thus

[tex]a_{n}[/tex] = [tex]\frac{31}{2}[/tex] + [tex]\frac{1}{2}[/tex] (n - 1) = [tex]\frac{15}{2}[/tex] + [tex]\frac{1}{2}[/tex] n - [tex]\frac{1}{2}[/tex] = [tex]\frac{1}{2}[/tex] n + 15