Mike built a sand castle that measured 484 centimetres by 386 centimetres, and dug a moat around it.Afterward, he decided to change the castle size, making it 725 centimetres by 314 centimetres.How much longer will the newer moat be than the older one?

Answer:

c = 20d + 15

Step-by-step explanation:

answer choices may help if the answer is not one of the choices; but here is the answer that it should be:

20 dollars per day is 20 times the length of rental.

15 is a cost that is added and does not change.

c = the total cost therefore:

c = 20d + 15

Answer:

Step-by-step explanation:

tan x-cot x

[tex]=\frac{sin~x}{cos~x} -\frac{cos~x}{sin ~x} \\=\frac{sin^2x-cos^2 x}{sin ~x~cos~x} \\=\frac{-2(cos^2x-sin^2x)}{2 sin ~x~cos~x} \\=\frac{-2 cos~2x}{sin~2x} \\=-2 cos ~2x~cosec~2x[/tex]

Answer:

[tex]r=\frac{44}{\pi }[/tex]

Step-by-step explanation:

[tex]88=2\pi r[/tex]

[tex]\mathrm{Switch\:sides}\\2\pi r=88\\\frac{2\pi r}{2\pi }=\frac{88}{2\pi }\\r=\frac{44}{\pi }\\or\\r=14.00563[/tex]

Answer:

2 metres

Step-by-step explanation:

Circumference = 2 × π × r

→ Substitute in the values

88 = 2 ×  [tex]\frac{22}{7}[/tex]  × r

→ Divide both sides by 2 to isolate  [tex]\frac{22}{7}[/tex]  and r

44 =  [tex]\frac{22}{7}[/tex]  × r

→ Multiply everything by 7 to get rid of the fraction

308 = 22 × 7r

→ Divide the equation by 22 to isolate 7r

14 = 7r

→ Divide the equation by 7 to isolate r

2 = r

The radius of the circle with a circumference of 88 meters is 2 metres

Answer:

x=5/13

Step-by-step explanation:

2/3+7/2=9x+5/6+4x

2/3+7/2-5/6=9x+4x

lcm of 2,3,6=6

2/3=4/6      7/2=21/6       5/6=5/6

4/6+21/6-5/6=9x+4x

30/6=13x

5=13x

x=5/13

Steps:

Step 1: Simplify both sides of the equation.

2/3−4x+7/2=−9x+5/6

2/3+−4x+7/2=−9x+5/6

(−4x)+( 2/3 + 7/2 )=−9x+ 5/6 (Combine Like Terms)

−4x+25/6=−9x+5/6

−4x+25/6=−9x+5/6

Step 2: Add 9x to both sides.

−4x+25/6+9x=−9x+5/6+9x

5x+25/6=5/6

Step 3: Subtract 25/6 from both sides.

5x+25/6−25/6=5/6−25/6

5x=−10/3

Step 4: Divide both sides by 5.

5x/5=−10/3/5

=  x=-2/3

Answer:  x=-2/3

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Hope this helps.

Answer:

Option (2).

Step-by-step explanation:

This question is incomplete; here is the complete question and find the figure attached.

In the diagram of a circle O, what is the measure of ∠ABC?

27°

54°

108°

120°

m(minor arc [tex]\widehat {AC}[/tex]) = 126°

m(major arc [tex]\widehat {AC}[/tex]) = 234°

By the intersecting tangents theorem,

If the two tangents of a circle intersect each other outside the circle, measure of angle formed between them is half the difference of the measures of the intercepted arcs.

m∠ABC = [tex]\frac{1}{2}[m(\text {major arc{AC})}-m(\text{minor arc} {AC})][/tex]

             = [tex]\frac{1}{2}(234-126)[/tex]

             = 54°

Therefore, Option (2) will be the answer.

Answer:

B.

Step-by-step explanation:

Answer:

12 square units

Step-by-step explanation:

formula= a+b/2×h

a=2

b=6

h=3

the answer will be = 2+6/2×3

=8/2×3

=4×3

=12

Answer:

17 square units i think

Answer:

[tex]-y^2+6y+16[/tex]

Step-by-step explanation:

[tex]-(y+2)(y-8)[/tex]

[tex]-1(y+2) \times (y-8)[/tex]

[tex](-y-2)\times (y-8)[/tex]

[tex]-y(y-8)-2(y-8)[/tex]

[tex]-y^2+8y-2y+16[/tex]

[tex]-y^2+6y+16[/tex]

Answer:

Initial population = 313

Population after 5 hours = [tex]3.36 \times 10^{11}[/tex]

Step-by-step explanation:

Let initial population = [tex]x[/tex]

It is given that population gets doubled every 10 minutes.

Population after 10 minutes = [tex]2x[/tex]

Population after 20 minutes = [tex]2^{2} x[/tex]

:

:

Population after 80 minutes = [tex]2^{8} x[/tex] and it is given as 80000.

[tex]\Rightarrow 2^{8} x = 80000\\\Rightarrow x = \dfrac{80000}{256}\\\Rightarrow x = 313[/tex]

So, initial population is 312.5 = ~313

To find, population after 5 hours i.e. 5 [tex]\times[/tex] 60 = 300 minutes

Population after 300 minutes =

[tex]2^{30} x\\\Rightarrow 2^{30} \times 313\\\Rightarrow 3.36 \times 10^{11}[/tex]

So, the answers are:

Initial population = 313

Population after 5 hours = [tex]3.36 \times 10^{11}[/tex]

Answer:

When we divide the inequality by 3 we get x < -2 so the answer is A.

Answer:

18 square meters

Step-by-step explanation:

Answer:

solution,

The given figure if a Trapezium whose parallel sides are of 3 m and 2 m respectively.

Distance between the parallels sides

i.e. height is 3 m

Now,

[tex]area = \frac{1}{2} \times sum \: of \: parallel \: sides \times height \\ = \frac{1}{2} \times (3 + 2) \times 3 \\ = \frac{1}{2} \times 5 \times 3 \\ = \frac{15}{2} \\ = 7.5 \: {m}^{2} [/tex]

Hope this helps...

Good luck on your assignment...

Answer:

The value of x is [tex]x=\frac{\log(2)}{\log(6)}[/tex].

Step-by-step explanation:

Solve the equation as follows:

[tex]4\times 6^{x}-7=1[/tex]

     [tex]4\times 6^{x}=7+1[/tex]

           [tex]6^{x}=\frac{8}{4}[/tex]

           [tex]6^{x}=2[/tex]

Take log on both sides.

[tex]\log(6^{x})=\log(2)[/tex]

[tex]x\log (6)=\log(2)[/tex]

        [tex]x=\frac{\log(2)}{\log(6)}[/tex]

Thus, the value of x is [tex]x=\frac{\log(2)}{\log(6)}[/tex].

Answer:

The answer is C 3- sqrt 11

Step-by-step explanation:

Answer:

Step-by-step explanation:

We will use the work form of a quadratic to determine what a is...in fact we will write the equation for the whole thing in the process, because it's part of solving for a.

y = ±|a|(x - h)² + k

where x and y are from a coordinate point on the graph, h and k are the coordinates of the vertex, the absolute value of a indicates how steep or flat the graph is compared to the parent graph, and the ± is because a positive parabola opens up and a negative one opens upside down.

The vertex is (0, 9) and the coordinate point I chose to use is (3, 0). Filling those in and solving for a:

0 = ±|a|(3 - 0)² + 9 and

0 = ±|a|(3)² + 9 and

-9 = ±|a|9 and

-1 = ±|a| so a = 1. Because this is an upside down parabola the negative is out front, but a is independent of it. The correct choice is C. The quadratic function is

[tex]y=-x^2+9[/tex] or in more detailed form:

[tex]y=-(x-0)^2+9[/tex]

Answer:

-2

Step-by-step explanation:

Answer:

The car travels 45 miles in one hour.

Step-by-step explanation:

Knowing that one hour is 60 minutes and that the car travels 0.75 miles every minute, you can multiply 60 and 0.75 which gives you 45 miles per hour meaning in one hour the car travels 45 miles.

Step-by-step explanation:

[tex]r = \sqrt{ \frac{ax - p}{q + bx} } \\ {r}^{2} = \frac{ax - p}{q + bx} [/tex]

r² (q + bx) = ax - p

qr² + bxr² = ax - p

qr² + p = ax - bxr²

qr² + p = x (a - br²)

[tex]x = \frac{q {r}^{2} + p}{a - b {r}^{2} } [/tex]

Answer:

[tex]\displaystyle x=\frac{-P-\math{R}^2Q}{\math{R}^2b-a}[/tex]

Step-by-step explanation:

[tex]R=\sqrt{\frac{ax-P}{Q+bx}}[/tex]

[tex]\mathrm{Square\:both\:sides}[/tex]

[tex]R^2=\left(\sqrt{\frac{ax-P}{Q+bx}}\right)^2[/tex]

[tex]R^2=\frac{ax-P}{Q+bx}[/tex]

[tex]\mathrm{Multiply\:both\:sides\:by\:}Q+bx[/tex]

[tex]\math{R}^2\left(Q+bx\right)=\frac{ax-P}{Q+bx}\left(Q+bx\right)[/tex]

[tex]\math{R}^2\left(Q+bx\right)=ax-P[/tex]

[tex]\math{R}^2Q+\math{R}^2bx=ax-P[/tex]

[tex]\mathrm{Subtract\:}\math{R}^2Q\mathrm{\:from\:both\:sides}[/tex]

[tex]\math{R}^2Q+\math{R}^2bx-\math{R}^2Q=ax-P-\math{R}^2Q[/tex]

[tex]\math{R}^2bx=ax-P-\math{R}^2Q[/tex]

[tex]\mathrm{Subtract\:}ax\mathrm{\:from\:both\:sides}[/tex]

[tex]\math{R}^2bx-ax=ax-P-\math{R}^2Q-ax[/tex]

[tex]\math{R}^2bx-ax=-P-\math{R}^2Q[/tex]

[tex]\mathrm{Factor}\:\math{R}^2bx-ax[/tex]

[tex]x\left(\math{R}^2b-a\right)=-P-\math{R}^2Q[/tex]

[tex]\mathrm{Divide\:both\:sides\:by\:}\math{R}^2b-a[/tex]

[tex]\frac{x\left(\math{R}^2b-a\right)}{\math{R}^2b-a}=-\frac{P}{\math{R}^2b-a}-\frac{\math{R}^2Q}{\math{R}^2b-a}[/tex]

[tex]x=\frac{-P-\math{R}^2Q}{\math{R}^2b-a}[/tex]

Answer:

Ryan had a head start of 10 meters

Answer:

Ryan had a head start of 10 meters.

Have a great day!

Step-by-step explanation:

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Answer:

2+3+10+15+20+2+30=82

82/8=10.25

Step-by-step explanation:+10.25

Answer:

The answer is 14.9

Step-by-step explanation:

First I added 2,3,10,15,20,24,30 then  divided it by 7.

Step-by-step explanation:

8 + 4x > 5x + 5

8 - 5 > 5x - 4x

3 > x

The solution to the system of equation is x < 3

Given the inequality expression 2(4+2x)>5x+5

Expand the inequality

2(4+2x)>5x+5

8 + 4x > 5x + 5

Collect the like terms

4x - 5x > 5 -8

-x > -3

x < 3

Hence the solution to the system of equation is x < 3

Learn more on inequality here: https://brainly.com/question/24372553

f(x)=x²−4x−21

The degree is the biggest power of x.  That's a polynomial of degree 2, also called a quadratic function.  Let's find its zeros.

0 = x²−4x−21 = (x - 7)(x+3)

x=7 or x=-3

The fundamental theorem guarantees every non-constant polynomial with complex coefficients has a complex zero, let's call it r.  If we divide the polynomial by x-r there won't be any remainder and we'll get a new polynomial, one degree less.  The fundamental theorem again applies and (if it's not a constant polynomial) we are assured of another zero, s.  We divide by x-s and get a new polynomial of degree one less.  We repeat all this until we get a constant polynomial (degree zero).    So we get a zero for every degree. They're not necessarily all different.

Answer:

The degree of f(x) is 2. The Fundamental Theorem of Algebra guarantees that a polynomial equation has the same number of complex roots as its degree. This means that f(x) has exactly 2 zeros. Those zeros are 7 and -3.

Answer:

C. (1,-1)

Step-by-step explanation:

Lines are intersecting each other at point (1, - 1).

Hence, the system of equations graphed here would be (1, - 1)

Answer:

8a^3.

Step-by-step explanation:

(a+b)^3=a^3+b^3+3a^2b+3ab^2

(a-b)^3=a^3-b^3-3a^2b+3ab^2

(a+b)^3+(a-b)^3=2a^3+6ab^2

According to the question

(a+b)^3+(a-b)^3+6a(a^2-b^2)

Put in the value

=2a^3+6ab^2 +6a^3–6ab^2

=8a^3

In the simplest form expression (a + b)³ + (a - b)³ + 6a(a² - b²) can be written as,  8a³

Algebraic identities are algebraic equations that are true regardless of the value of each variable. Additionally, they are employed in the factorization of polynomials. Algebraic identities are employed in this manner for the computation of algebraic expressions and the solution of various polynomials.

Given that,

A algebraic identity,

(a + b)³ + (a - b)³ + 6a(a² - b²)

It is known that,

(a + b)³  = a³ + b³ + 3ab(a + b)

(a - b)³  =  a³ - b³ - 3ab(a - b)

So, now we can substitute expressions

(a + b)³ + (a - b)³ + 6a(a² - b²)

a³ + b³ + 3ab(a + b) + a³ - b³ - 3ab(a - b) +  6a(a² - b²)

a³ + b³ +  3a²b + 3ab² + a³ - b³ -3a²b + 3ab² + 6a³ - 6ab²

8a³

Hence, the simplest form is 8a³

To know more about algebraic expressions check:

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The right answer is 7/3

please see the attached picture for full solution

hope it helps..

Good luck on your assignment

Answer:

[tex]slope = \frac{7}{3} [/tex]

Step-by-step explanation:

[tex](5 \: \: , \: \: 9) = > (x1 \: \: \:, \: y1) \\ (2 \: \: , \: \: 2) = > (x2 \: \: \:, \: \: y2)[/tex]

[tex] slope \\ = \frac{y1 - y2}{x1 - x2} \\ = \frac{9 - 2}{5 - 2} \\ = \frac{7}{3} [/tex]

hope this helps

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Answer:

4

Step-by-step explanation:

g(3) = -2(3)^2 -4 = 2(9) -4 = 18-4 = 14

|f(2)| = | 2^2 -3| = | 4-3| = 1

(g(3) +2) = (14+2) = 16

4*  |f(2)|  = 4*1 = 4

16/4 = 4

Answer:

The volume of the sphere is 32 π /3 cm^3

Step-by-step explanation:

Mathematically, the volume of a sphere can be calculated using the formula below;

V = 4/3 * pi * r^3

Now since we have the radius and diameter = 2 * radius

radius = diameter/2 = 4/2 = 2

Substituting this value into the volume equation;

V = 4/3 * pi * 2^3 = 32pi/3

Answer:

The correct answer is A

Step-by-step explanation:

Answer:

To eliminate y- terms

Multiply equ(1) by 3 and equ(2) by -4

To eliminate y- terms

Multiply (1) by 3 and (2) by -5

Step-by-step explanation:

5x - 4y = 28 (1)

3x - 3y = 30 (2)

To eliminate y- terms

Multiply equ(1) by 3 and equ(2) by -4

15x-12y=84

-12x+12y= -120

Add equ (3) and (4)

3x=84-120

3x=-36

x=-36/3

= -12

x=-12

To eliminate x- terms

5x-4y=28

3x-3y=30

Multiply (1) by 3 and (2) by -5

15x-12y=84

-15x+15y=-150

Add the new equation

3y= -66

y= -22

Answer:

The fourth choice is the correct one.

Step-by-step explanation:

If the count of negative signs is even, the product is even (positive).

This does not apply to the first choice; this expression is odd.

Same for the second choice.

Same for the third choice.  The expression is odd.

The fourth choice is POSITIVE because there are an even number (2) of negative signs.

Answer:a

Step-by-step explanation:

Answer:

The answer is A.

Step-by-step explanation:

Pythagorean theorem.

a^2+b^2=c^2.

2^2+3^2=d^2

Answer:

240 degrees

Step-by-step explanation:

Mathematically, the area of a circle is

A = 2 * pi * r^2

we need to calculate the radius of the circle first

18pi = 2pi * r^2

divide both sides by 2pi

r^2 = 9

r = 3 inches

Area of sector = angle/360 * pi * r^2

6pi = angle/360 * pi * 3^2

6pi = angle/360 * 9pi

(360 * 6pi)/9pi = angle

40 * 6 = 240 degrees