Santiago is eight years younger than Juan is today. If, in four years, Santiago will be half Juan’s age, how old is Santiago today? a) 1 b) 2 c) 3 d) 4

Answer:

[tex]10i\sqrt{2r}[/tex].

Step-by-step explanation:

[tex]5\sqrt{-8r}[/tex]

= [tex]5\sqrt{-1 * 2 * 2 * 2 * r}[/tex]

= [tex]5i\sqrt{2^2 * 2 * r}[/tex]            (i = the square root of -1)

= [tex]5i * 2\sqrt{2 r}[/tex]

= [tex]10i\sqrt{2r}[/tex]

Hope this helps!

Answer:

5/9 is the simplest fraction for this ratio

Answer:

Step-by-step explanation:

The rate at which distance is increasing between the birds is ...

  r = d/t = (402 mi)/(6 h) = 67 mi/h

This is the sum of the speeds of the two birds, so is 15 mph more than double the speed of the slower bird. That bird's speed is then ...

  (67 -15)/2 = 26 . . . miles per hour

The faster bird is 15 mph faster so is 26+15 = 41 mph.

The slower bird's speed is 26 mph; the faster bird's speed is 41 mph.

Answer:

3^1 or 3

3^5 * 3^-4 are 3^5-4

so, 3^1!

Hope it helps!

Answer:

3^1

Step-by-step explanation:

Since the bases are the same and we are multiplying we can add the exponents

a^b * a^c = a^(b+c)

3^5 * 3^-4

3^ (5+-4)

3^1

Answer: (16,O0) That is 16 to positive infinity

Step-by-step explanation:

4.5x - 9.5 > 62.5

4.5x > 62,5 + 9.5

4.5x > 72

x > 72/ 4.5

x> 16

So all real numbers greater than 16 is the solution set.

(16,O0)

I wish I had the infinity symbol on this keyboard!

Answer:

-7

Step-by-step explanation:

-1.68j+1.24=13

-1.68j=13-1.24

-1.68j=11.76

j=11.76/-1.68

j=-7

Hi there! Hopefully this helps!

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Answer: j = -7

You can also rewrite the equation(replace "j" with the answer):

-1.68(-7) + 1.24 = 13.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

How I solved it:

-1.68j + 1.24 = 13.

We subtract 1.24 from both sides.

-1.68j = 13 - 1.24

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-1.68j = 13 - 1.24

We subtract 1.24 from 13 to get 11.76.

-1.68j = 11.76

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

-1.68j = 11.76

We then divide both sides by -1.68.

j = [tex]\frac{11.76}{-1.68}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~  

Expand [tex]\frac{11.76}{-1.68}[/tex] ≈ -7 by multiplying both the numerator and the denominator by 100.

j = [tex]\frac{1176}{-168}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Divide 1176 by -168 to get -7.

Answer:

B. (m-1)(m-8)

Step-by-step explanation:

The factors of 8 (constant term) are

{(1,8), (2,4)}, from which we see that 1+8 = 9, the absolute value of the coefficient of the second term.

Therefore we can group the expression as

m^2 - 9m + 8

= m^2-m - (8m -8)

then factor each group

= m(m-1) - 8(m-1)

and factor out (m-1)

= (m-1)(m-8)

we need a picture of the weather data

Answer:

Step-by-step explanation:

Given two  series A and B;

Series A: 10 + 4 +8/5 + 16/25 + 13/125 + ...

Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...

Both series are geometric series since they have the same common ratio. Given the geometric series T₁, T₂, T₃, T₄..., the common ratio r is expressed as [tex]\frac{T_2}{T_1} =\frac{T_3}{T_2} =\frac{T_4}{T_3} = r[/tex].

a) For series A, Given T₁ = 10, T₂ = 4, T₃ = 8/5 and T₄ = 13/125

Its common ratio is expressed as [tex]\frac{4}{10} =\frac{8/5}{4} =\frac{13/125}{8/5} = 2/5[/tex]

Hence the common ratio of series A is 2/5

The sum to infinity of the geometric series will be expressed as [tex]s_\infty = \dfrac{a}{1-r}[/tex]

Note that the sum to infifnity is used since the series is tending to infinity.

a is the first term if the series = 10

r - 2/5

On substituting this values into the formula;

[tex]s_\infty = \dfrac{10}{1-2/5} \\\\s_\infty = \dfrac{10}{3/5} \\\\s_\infty = 10* 5/3\\s_\infty = 50/3[/tex]

Hence the sum of the series is 50/3

b) For the series B;

Series B: 1/5 + 3/5 + 9/5 + 27/5 + 81/5 +...

The common ratio of the series is expressed as shown;

[tex]\frac{3/5}{1/5} =\frac{9/5}{3/5}= \frac{27/5}{9/5 } = r\\ r = (3/5 * 5/1) = 9/5*5/3 = 27/5*5/9 = 3[/tex]

Hence its common ratio is 3.

Sun of the series is expressed similarly as:

[tex]s_\infty = \frac{a}{1-r}\\ s_\infty = \frac{1/5}{1-3}\\\\s_\infty = \frac{1/5}{-2}\\\\[/tex]

[tex]s_\infty = 1/5 * -1/2\\s_\infty = -1/10[/tex]

Hence the sum of series B is -1/10

Answer:

NQ=15, NP=20

Step-by-step explanation:

9/(2x+1)=12/(3x-1)

cross product

12(2x+1)=9(3x-1)

24x+12=27x-9

12=27x-24x-9

12=3x-9

3x=12+9

3x=21

x=21/3

x=7

NQ=2x+1=2(7)+1=15

NP=3x-1=3(7)-1=21-1=20

Answer:

x = 7

Step-by-step explanation:

Since the triangles are similar the ratio of the sides must be the same

AB           AK

------- = --------------

QN            NP

9                12

---------- = ------------

2x+1             3x-1

Using cross products

9(3x-1) = 12(2x+1)

Distribute

27x -9 = 24x +12

Subtract 24x from each side

3x-9 = 12

Add 9 to each side

3x = 21

Divide by 3

x = 7

Answer: C) 16

Step-by-step explanation:

A Hexagon has 6 Sides and Since the perimeter is 24, each side has a length of 4.

4 * 4 = 16

Answer:

(-8.64) / (-0.024) = 360

Step-by-step explanation:

You have to type like this in your question;

(-8.64) / (-0.024)

or [tex]\frac{-0.024}{-8.64}[/tex].

Bye!

Answer:

lets start with finding the slope

m=7-(-1)/4-3

m=8

now we can choose either of the 2 points given and the slope and plug that into the point slope form

y-7=8(x-4)

y-7=8x-32

y=8x-25

and that is your equation

Answer:

y = 8x - 25

Step-by-step explanation:

The equation of a line is y = mx + b

To find the slope use y2-y1/x2-x1

When you plug it in it will be 7 + 1/4 - 3 (8)

Now it is y = 8x + b

Lastly you need to plug in a coordinate to the equation to find b

7 = 8(4) + b (-25)

Answer: A.71

Step-by-step explanation: 1.set up the equation

2. 4n-18+n+9=151-5n

3.combine like terms ->  5n-9=151-5n

4.solve for n

5.10n=160

n=16

now you have to plug 16 in for n in order to get the remote exterior angle.

151-5(16)

151-80

71°

The sum of any two interior angle is equal to the third exterior angle. The value of n will be 16°. Then the correct option is B.

A triangle is a three-sided polygon with three angles. The angles of the triangle add up to 180 degrees.

The triangle having the interior angle x and y, and z is the exterior angle of triangle.

m∠x = (4n − 18)°, m∠y = (n + 9)°, and m∠z = (151 − 5n)°

Then the value of n will be

We know that the sum of any two interior angle is equal to the third exterior angle. Then we have

∠x + ∠y = ∠z

4n - 18 + n + 9 = 151 - 5n

10n = 160

n = 16°

Then the correct option is B.

More about the triangle link is given below.

https://brainly.com/question/25813512

#SPJ2

Answer:

300 yards squared

Step-by-step explanation:

Triangle area = 12 x 5 / 2 = 30

2 Triangles (because there are two of them) = 60

Big rectangle = 8 x 13 = 104

Small Rectangle = 8 x 5 = 40

Medium Rectangle = 96

Add all up = 300

Hope that helped!!! k

They do. the initial point is same in both lines.

formally,

[tex] \vec{r_1}=(2\hat i+3 \hat j+\hat k)+s(4\hat i-\hat k)[/tex]

$\vec{r_2}=(2\hat i +3 \hat j +\hat k)+t(2\hat i+2\hat j +\hat k)$

if they intersect then $\begin{vmatrix} 4 & 0 & -1 \\ 2 & 2 & 1 \\ (2-2) & (3-3) & (1-1) \end{vmatrix}=0$

(which obviously is zero)

Answer:

answer is b

Step-by-step explanation: i am sure of it

Answer:

D. 15

Step-by-step explanation:

Both equations need the same end result because this is a square:

3x - 15 = 45 - x =

3x - 3x = 45 - x - 3x

0 = 45 - 4x

4x = 60

4x/4 = 60/4 =

X = 15

Check:

3(15) - 15 = 45 - 15

45 - 15 = 45 - 15

30 = 30

Hi there! :)

Answer:

[tex]\sqrt{\frac{A}{\pi } } = r[/tex]

Step-by-step explanation:

Formula for the area of a circle:

[tex]A = \pi r^{2}[/tex]

Rearrange the equation in terms of "r":

Divide 'π' from both sides:

[tex]\frac{A}{\pi } = r^{2}[/tex]

Take the square root of both sides:

[tex]\sqrt{\frac{A}{\pi } } = r[/tex]

Answer:

[tex]r = \sqrt{ \frac{A}{ \pi}}[/tex]

Step-by-step explanation:

[tex]A =\pi r^2 \\Divide\: both \:sides\:of\:the\:equation \\\frac{A}{ \pi} =\frac{ \pi r^2}{ \pi} \\r^2 = \frac{A}{ \pi} \\\sqrt{r^2} =\sqrt{ \frac{A}{ \pi}} \\\\r = \sqrt{ \frac{A}{ \pi}}[/tex]

Answer:

[tex]\huge\boxed{Second\ Number = 42}[/tex]

Step-by-step explanation:

Let the consecutive even numbers be x,x+2,x+4, x+ 6, x+ 8 and x+10

So, the given condition is:

x+x+2+x+4+x+6+x+8+x+10 = 270

6x + 30 = 270

Subtracting both sides by 30

6x = 270 - 30

6x = 240

Dividing both sides by 6

x = 40

So,

First Number = x = 40

Second Number = x+2 = 40+2 = 42

Third Number = x+4 = 40+4 = 44

Fourth Number = x+6 = 40+6 = 46

Fifth Number = x+8 = 40+8 = 48

Sixth Number = x+10 = 40+10 = 50

Answer:

22 I think

Step-by-step explanation:

Answer:

3 uhhh i have to write 20 letters so aha nice

[tex]\dfrac{x}{4}=\dfrac{x+9}{4+12}\\\\16x=4(x+9)\\16x=4x+36\\12x=36\\x=3[/tex]

The volume of the pyramid is 1,280 cubic feet. Thus, the correct option is A.

Let h be the height of the pyramid, l be the slant height, and A be the base area of the pyramid. Then the volume of the pyramid will be given as,

Volume = (1/3) × A × h

The slant height is given as,

l² = (half of the side)² + h²

Given that:

Slant height, l = 17 ft

Side length, a = 16 ft

The height of the pyramid is calculated as,

17² = (16/2)² + h²

h = 15

The volume of the pyramid is calculated as,

V = 1/3 x 16 x 16 x 15

V = 256 x 5

V = 1,280 cubic feet

Thus, the correct option is A.

More about the volume of the pyramid link is given below.

https://brainly.com/question/17615619

#SPJ3

Answer:

$900

Step-by-step explanation:

First, find the area of the floor with the equation A = lw

A = lw

A = (20)(20)

A = 400 ft²

Since each tile covers 1 sq ft and the floor's area is 400 sq ft, they will need 400 tiles.

To calculate the total cost, multiply 400 by 2.25

400(2.25) = 900

= $900

Answer:

see explanation

Step-by-step explanation:

f(g(2)) = f(0) = -2

g(f(1)) = g(0) = 0

Answer:

The correct answers for both of them is -2 and 0.

Step-by-step explanation:

I)

[tex](f\circ g)(2)=f(g(2))[/tex]

From the red graph, we can see that g(2) is 0.

Therefore, f(g(2)) is equal to f(0).

And from the blue graph, we can see that f(0) is -2.

Therefore:

[tex](f\circ g)(2)=-2[/tex]

II)

[tex](g\circ f)(1)=g(f(1))[/tex]

From the blue graph, we can see that f(1) is 0.

Therefore, g(f(1)) is equal to g(0).

And from the red graph, g(0) is 0.

Therefore:

[tex](g\circ f)(1)=0[/tex]

So, you got one correct. Nicely done!

Answer:

B) The vertex will shift down.

Step-by-step explanation:

In the equation of a parabola, (y - k)² = 4p(x - h), (h, k) is the vertex.

The original parabola's vertex was (3, -2).

In the new parabola, the y-coordinate changed to -10, making the new vertex (3, -10).

So, the parabola's vertex shifted down 8 units from -2 to -10.

Answer:

16,20,8,36

Step-by-step explanation:

he plans to have 2 tables for every 8 guest, which means 1 table for each 4 guest!

now:

2(tables)×4(number of people at each table)=8(number of guests

4×4=16

5×4=20

32(number of guests)÷4(number of people at each table)=8(number of tables)

9×4= 36

Answer:

Since there are 8 guests every 2 table we need to find how many guests are in one table:

8 ÷ 2 = 4 guests

4 tables = 4 x 4 = 16 guests

5 tables = 5 x 4 = 20 guests

32 guests = 32 ÷ 4 = 8 tables

9 tables = 9 x 4 = 36 guests

Hope this helps :D

Answer:

[tex]4 \sqrt{6}[/tex]

Step-by-step explanation:

The question is not properly presented and has mission options; however, the solution is as follows

Given

[tex]\sqrt{96}[/tex]

Required

Simplify

[tex]\sqrt{96}[/tex]

Start by expanding

[tex]\sqrt{16 * 6}[/tex]

The expression can be split to:

[tex]\sqrt{16} * \sqrt{6}[/tex]

Take positive square root of 16

[tex]4 * \sqrt{6}[/tex]

[tex]4 \sqrt{6}[/tex]

The expression cannot be further simplified

Answer:

36

Step-by-step explanation:

There would be three on each edge. (Five, minus the two ends that have 3 sides painted.)

A cube has 12 edges.

12x3=36

Answer:

  2 triangles

Step-by-step explanation:

The given angle is opposite the shorter of the given sides, so the number of triangles is 2. (30/25·sin(42°) ≈ 0.8 < 1)

_____

Additional comment

For the case where the shorter given side is opposite the given angle, there is the possibility that the triangle could be a right triangle (1 solution) or that there may be no solutions. You can tell the difference by computing ...

  (long side)/(short side) × sin(given angle)

If this result is exactly 1, the triangle is a right triangle. If it is greater than 1, the triangle cannot exist (no solutions). Since the sines of most angles are irrational, it is unlikely you will see this result be exactly 1 (except for a 30°-60°-90° right triangle).

These observations are a consequence of the Law of Sines, which tells you ...

  sin(A) = (a/b)sin(B)

For real angles, sin(A) ≤ 1.

Answer:

2

Step-by-step explanation:

A coefficient is the number placed before the variable. The variable gets multiplied by the coefficient.

The format is not exactly clear with the expression in the question.

Assuming the expression is '8 * 2n', the coefficient would be 2.

'n' is getting multiplied by '2'.

'8' does not have a variable next to it, so it is just a term in the expression.

The product of 8 and 2 is 16. 16 is not in the expression.

If the expression was '8.2n', 8.2 would be the coefficient.

Brainilest Appreciated.