mathematic question

Answer:

Let's define East as the positive x-axis and North as the positive y-axis.

If Michelle's initial position is (0, 0)m

We know that Nathasha is 50m due East of Michelle.

Then the position of Natasha is (50, 0)m

Now we know that Natasha walks 20m due North, then the new position of her's is:

(50, 0 + 20)m = (50, 20)m

While Michelle walks 10m due South (South would be the negative y-axis, then we subtract 10 meters)

Michelle's new position will be:

(0, 0 - 10)m = (0, -10)m

Now we want to know the distance and bearing of Michelle from Natasha.

First, remember that the distance between two points (a, b) and (c, d) is given by:

Distance = √( (a - c)^2 + (b - d)^2)

Then the distance between Michelle and Natasha is:

Distance = √( (50m - 0m)^2 + (20m - (-10m))^2)

Distance = √( (50m)^2 + (30m)^2) = 58.31m

Now to find the bearing you can see the image below:

Point B is Michelle's position and point A is Natasha's position.

To find the bearing, we can make a triangle rectangle as the one shown in the image:

Also remember the relation:

Tan(a) = (opposite cathetus)/(adjacent cathetus).

Where the opposite cathetus is the difference between the x-values of each position, this is:

opposite cathetus = 50m - 0m = 50m

And the adjacent cathetus is the difference between the y-values, this is:

adjacent cathetus = 20m - (-10m) = 30m

Then:

Tan(a) = 50m/30m

Tan(a) = 5/3

Now if we apply the inverse Tan function to both sides, Atan(x) we get:

Atan(Tan(a)) = Atan(5/3)

a = Atan(5/3) = 59°

So the bearing is of 59°.

Answer:

B

Step-by-step explanation:

firstly as we know that,

nth term of an A.P. is n= a1 + (n-1)d

here d is -3 so, A1 = 1-(-3) = 4

so, 5th term = 4 + ( 5-1)( -3) = 4 + 4(-3) = 4 - 12 = -8

so the answer is -8 which is option B.

Hope this answer helps. I got a little help from my tutors on Gauthmath app which is really good. you can check it out too. :)

Answer:

a

Step-by-step explanation:

I think so..

Answer:

k = -2

Step-by-step explanation:

f(x) = (x − h)² + k

(h, k) is the (x, y) coordinate of the vertex

For a vertex of (4, -2)

h = 4

k = -2

Answer:

4/12

Step-by-step explanation:

add up all the marbles, and take how many blue marbels there are and put both numbers in fraction form

Answer:14 m

Step-by-step explanation:

Dada

larga [tex]l=20\ m[/tex]

superficie [tex]A=280\ m^2[/tex]

Suponga que el ancho es w

La superficie está dada por el producto de la longitud y la anchura.

[tex]\therefore A=lw\\\Rightarrow 280=20\times w\\\Rightarrow w=14\ m[/tex]

Por lo tanto, el ancho es de 14 m.

Answer:

Step-by-step explanation:

-6 and up going left

Answer:

63

Step-by-step explanation:

mark me brainliest plzzz

[tex]\sf\purple{The\:value\:of\:x\:is\:63.}[/tex]

[tex]\large\mathfrak{{\pmb{\underline{\red{Step-by-step\:explanation}}{\orange{:}}}}}[/tex]

[tex] \frac{3}{8} = \frac{x}{168} \\ \\ ✒ \: \frac{3 \times 168}{8} = x \\ \\ ✒ \: \frac{504}{8} = x \\ \\✒ \: 63 = x[/tex]

Therefore, the value of [tex]x[/tex] is 63.

[tex]{ \bf{ \underbrace{To\:verify:}}}[/tex]

[tex] \frac{3}{8} = \frac{63}{168}\\ \\✒ \: 0.375 = 0.375 \\ \\✒ \: L.H.S.=R. H. S [/tex]

Hence verified. ✔

[tex]\large\mathfrak{{\pmb{\underline{\orange{Happy\:learning }}{\orange{!}}}}}[/tex]

Answer:

8

Step-by-step explanation:

write numbers in numerical order then subtract the highest number from the lowest number and you get the range.

(1,2,3,3,4,4,6,9)

9 - 1 = 8

Answer:

3^-6(81)^2=3^-6(6561)=9 which is 3^2

Answer: 68,819 rabbits

Step-by-step explanation:

First find the annual rate of growth that took the number of rabbits from 9,400 in 1998 to 32,000 in 2006.

Use the future value formula:

Number of years = 2006 - 1998 = 8 years

Future value formula:

Future value = Current value * ( 1 + rate) ^ number of years

Assume 2006 is the future and 1998 is present.

32,000 = 9,400 * (1 + r) ⁸

32,000 / 9,400 = (1 + r)⁸

(1 + r)⁸ = 3.404255319

1 + r = ⁸√3.404255319

r = ⁸√3.404255319 - 1

r = 16.55%

Use that rate to find the number of rabbits in 2011:

= Current value * (1 + rate) ^ number of years

Number of years = 2011 - 2006 = 5 years

= 32,000 * ( 1 + 16.55%)⁵

= 68,819 rabbits

Answer:

5x^2 - 3x -5

Step-by-step explanation:

You simplify the like terms

Remember to use distributive property to do the (7x-3x^2+5) part

Given:

The height, in feet, of each rocket at t seconds after launch is given by the polynomial equations:

Rocket A: [tex]-15t^2+100t[/tex]

Rocket B: [tex]-14t^2+85t+3[/tex]

To find:

The equation to find the "difference" in height of Rocket A and Rocket B.

Solution:

The difference in height of Rocket A and Rocket B is:

Difference = Height of Rocket A - Height of Rocket B

[tex]\text{Difference}=(-15t^2+100t)-(-14t^2+85t+3)[/tex]

[tex]\text{Difference}=-15t^2+100t+14t^2-85t-3[/tex]

[tex]\text{Difference}=(-15t^2+14t^2)+(100t-85t)-3[/tex]

[tex]\text{Difference}=-t^2+15t-3[/tex]

Therefore, the difference in height of Rocket A and Rocket B is [tex]-t^2+15t-3[/tex].

Answer:

See Explanation

Step-by-step explanation:

The question is incomplete, as the prisms and the riddle are not given.

The riddle aspect of the question cannot be attempted, else there are clues.

So, I will give a general rule on how to calculate the surface areas of prisms.

For rectangular prisms, the surface area is:

[tex]Area = 2*(Length * Width + Length * Height + Width * Height)[/tex]

For the attached rectangular prism, the area is:

[tex]Area = 2 *(10*11 + 11 * 15 + 10 * 15)[/tex]

[tex]Area = 2 *(425)[/tex]

[tex]Area = 850m^2[/tex]

For triangular prisms, the surface area is:

[tex]Area = L + 2 * B[/tex]

Where

[tex]L \to[/tex] Lateral Area

[tex]B \to[/tex] Base Area

The area of the attached triangular prism is:

[tex]L = (a + b + c) * h[/tex]

[tex]L = (6 + 8 + 10) * 12[/tex]

[tex]L = 24 * 12[/tex]

[tex]L = 288[/tex]

[tex]B = \frac{1}{2} * bh[/tex]

[tex]B = \frac{1}{2} * 6 * 8[/tex]

[tex]B = 24[/tex]

So, we have:

[tex]Area = L + 2 * B[/tex]

[tex]Area = 288 + 2 * 24[/tex]

[tex]Area = 288 + 48[/tex]

[tex]Area = 336ft^2[/tex]

Answer:

B

Step-by-step explanation:

mulitiply by 2

Answer:

Step-by-step explanation:

3 = 1(1 + x)^4

let q = 1 + x

3 = q^4

ln(3)  = 4  ln(q)

ln(3)/4 = ln(q)

.274 = ln(q)

q = e^.274 = 1.316

x = .316

Future amount = 48(1+.316)^4

Future amount = 143.96

Hope this helps please mark me brainliest

Answer:

x = -3

Answer:

The mean increases by 2.

Step-by-step explanation:

Answer:

B.

Step-by-step explanation:

28 is not a multiple of 13.

Answer:

Brandon is correct

Step-by-step explanation:

Brandon is running errands for his mother.

It is 1/4 mile from his house to the library and 2/3 mile from the library to the grocery store .

Brandon claims that he walked a total of 11/12 mile if he goes from his house to the library to the grocery store.

Distance from his house to the library = 1/4 mile

Distance from the library to the grocery store = 2/3 mile

Total distance Brandon walks from his house to the library to the grocery store = Distance from his house to the library + Distance from the library to the grocery store

= 1/4 + 2/3

Make both 1/4 and 2/3 have the same denominator to be able to add

The lowest common multiple (LCM) of 4 and 3 is 12

Therefore,

1/4 + 2/3

= (3+8)/12

= 11/12

Total distance Brandon walks from his house to the library to the grocery store = 11/12 mile

Given:

Consider the expression is:

[tex]\sqrt{-9}[/tex]

To find:

The equivalent expression.

Solution:

We have,

[tex]\sqrt{-9}[/tex]

It can be written as:

[tex]\sqrt{-9}=\sqrt{-1\times 9}[/tex]

[tex]\sqrt{-9}=\sqrt{-1}\times \sqrt{9}[/tex]

[tex]\sqrt{-9}=i\times 3[/tex]                 [tex][\because \sqrt{-1}=i][/tex]

[tex]\sqrt{-9}=3i[/tex]

The expression [tex]3i[/tex] is equivalent to the given expression.

Therefore, the correct option is A.

Answer:

The triangles are congruent  by HL

Step-by-step explanation:

The triangles are right triangles so we can use either HL ( hypotenuse leg) or LL (leg leg) if we know that two sides are congruent

We know one leg is equal to the other by the red line.  The hypotenuse is the same since it is the same line.

The triangles are congruent  by HL

Answer:

10

Step-by-step explanation:

5 (2) is the same as 5 × 2 which equals 10

Answer:

Step-by-step explanation:

Given here,

(5)2

= 5 × 2.

= 10 (Ans)

Answer:

35

Step-by-step explanation:

Only if u put x as 35 will the whole triangle sum equal 180 as necessary for the theorem to be true.

Answer:

Lower Bound = 2.996

Upper bound = 3.244

Step-by-step explanation: