Express in scientific notation,
458,700
4,587 * 10 5
4,587 * 104
4,587 * 104
4,587 * 106

Answer:

4181

Step-by-step explanation:

The Fibonacci sequence starts with 0 and 1... then all other terms are obtained by adding the two previous terms.

0, 1, 1, 2, 3, 5, 8, 13, 21, and so on.

So, if you have any two consecutive terms from the sequence, you can easily find the next one by adding them together:

F(19) = F(17) + F(18)

F(19) = 1597 + 2584  = 4181

Answer:

C

Step-by-step explanation:

By observation, and inspecting the 2 given points closely, we can immediately see that both points have  y = -2 as common y-ordinates .

This means that the horizontal  line y =-2 joins these 2 points.

Answer C is correct.

Answer:

C

Step-by-step explanation:

use slope formula and slope-intercept form Y=mx=b

Answer:

a= 2, b= 3, c= 7

Step-by-step explanation:

Given the quadratic equation:

Quadratic equation in general form is:

Comparing the two above we can get following coefficients:

a= 2

b= 3

c= 7

A= 4

B= 12

C= 9

Theese are correct

Answer:

[tex]g(n)=18-4n[/tex]

Step-by-step explanation:

You are given the function g, for which

[tex]g(1)=14,\\\\g(n)=g(n-1)-4[/tex]

Find some values of this function:

[tex]g(1)=14\\ \\g(2)=g(2-1)-4=g(1)-4=14-4=10\\ \\g(3)=g(3-1)-4=g(2)-4=10-4=6\\ \\g(4)=g(4-1)-4=g(3)-4=6-4=2\\ \\...[/tex]

You can see that ecah next value is 4 less than previous one, so these values form an arithmetic sequence and you have to find the nth term of this sequence. The nth term of arithmetic sequence is

[tex]a_n=a_1+(n-1)d,[/tex]

where

[tex]a_1=g(1)=14\\ \\d=-4[/tex]

So,

[tex]g(n)=a_n=14+(n-1)\cdot (-4)=14-4n+4=18-4n[/tex]

Answer:

18-4n

Step-by-step explanation:

You can also just multiply by the decimal equivalent.

12*.35=4.2

35% of 12 is 4.2

Hope this helps!

Answer:

4.2

Step-by-step explanation:

Find 35% of 12. ​

To find 35% of 12, you can use the method you demonstrated above by solve

35% = 35/100

of 12 = multiplication.

35/100 × 12

0.35 × 12

= 4.2

        OR

35 × 12/100

420/100

= 4.2  ​

Hope this helps!

Thanks.

Answer:

B if you mean (-2)^(-3)

Step-by-step explanation:

(-2)-3=-5

But based on the answers I think you meant to write (-2)^(-3)

which means 1/(-2)^3

So we have 1/(-2*-2*-2)=1/-8 or -1/8

Answer:

B. -1/8.

Step-by-step explanation:

I guess you mean (-2)^-3

= 1 / (-2)^3

= 1 / -8

= -1/8.

Answer:

Step-by-step explanation:

Given that the park is 6 miles due west of your house, and the library is 11 miles north of your house.

Thus the park and library forms the legs of a right triangle with shortest distance being the hypotenuse (provided there are no buildings in between)

We can use pythagoren theorem to find the shortest distance i.e. hypotenuse.

Shortest distance^2 =[tex]\sqrt{6^2+11^2} =\sqrt{197}[/tex]

We find that square root is 14.03

Thus shortest distance is 14 miles.

The shortest distance from the park to the library is 12.53 miles.

It is the measure of the length between the two points. It is a scalar quantity.

It is a type of triangle in which one angle is 90 degrees and it follows the Pythagoras theorem and we can use the trigonometry function.

Given

The park is 6 miles due west from your house.

And the library is 11 miles north of your house.

The shortest distance from the park to the library.

Perpendicular P = 11

Bas B = 6

We know the Pythagoras theorem.

H² = P² + B²

H² = 11² + 6²

H² = 121 + 36

H² = 157

H = 12.53

Thus, The shortest distance from the park to the library is 12.53 miles.

More about the distance link is given below.

https://brainly.com/question/989117

Answer

Average/Mean: 13.7 pools

Step-by-step explanation:

When asked to find the average number of anything, you are trying to find the mean.

The Arithmetic Mean is the average of the numbers: a calculated "central" value of a set of numbers.  

To calculate it:  

• add up all the numbers,  

• then divide by how many numbers there are.

Answer:

9+sqrt(14)

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

9+sqrt(14)

Step-by-step explanation:

To get rid of the square root in the denominator, you want to multiply by the conjugate.

Since we have a - sqrt(b) in the denominator

We need to multiply by a + sqrt(b)

What we do the bottom, we do to the top

9+sqrt(14)

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

9+sqrt(14)

ANSWER

[tex]f(a + 2) = \frac{a + 5}{a - 1} [/tex]

EXPLANATION

The given function is

[tex]f(x) = \frac{3 + x}{x - 3} [/tex]

To find f(a+2) we substitute x=a+2.

That is wherever we see 'x' we replace it with 'a+2'

[tex]f(a + 2) = \frac{3 + a + 2}{a + 2 - 3} [/tex]

We simplify further to obtain:

[tex]f(a + 2) = \frac{a + 5}{a - 1} [/tex]

This is defined for

[tex]a \ne1[/tex]

Answer:  [tex]\bold{y=\dfrac{59}{34}}[/tex]

Step-by-step explanation:

   5x + 2y = 7   ⇒   2(5x + 2y = 7)   ⇒   10x +  4y  =  14

  -2x + 6y = 9  ⇒   5(-2x + 6y = 9)  ⇒  -10x + 30y = 45

                                                                         34y = 59

                                                                       ÷34   ÷34

                                                                             y = 59/34

Answer:

y=59/34

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

The slope is 2

Y int is -3

Area of rectangle is the product of its length and breadth. It is measured in unit squared. When the length and breadth are increased by 2 feet then the area of the given rectangular patio becomes 88 sq ft.

A rectangular patio is 9 ft by 6 ft.

The length of the rectangular patio is 9 ft.

The breadth of the rectangular patio is 6 ft.

Area of rectangle is the product of its length and breadth. It is measured in unit squared

The equation is given for the problem is,

[tex](6 + x)(9 + x) = 88[/tex]

On solving the above equation we get,

[tex]x^2+6x+9x+54= 88[/tex]

[tex]x^2+15x+54-88=0[/tex]

[tex]x^2+15x-34=0[/tex]

Find the value of x by using split the middle term method,

[tex]x^2+17x-2x-34=0[/tex]

Using the split the middle term method we get the two factor,

[tex](x+17)(x-2)=0[/tex]

Equate the above equation to zero we get the values of the x are -17 and 2.

Taking positive value of x and keeping it into the given equation we get,

[tex](6 + x)(9 + x) = 88[/tex]

[tex](6 + 2)(9 + 2) = 88[/tex]

[tex]8\times 11=88[/tex]

[tex]88=88[/tex]

Hence When the length and width are increased by 2 feet then the area of the given rectangular patio becomes 88 sq ft.

Learn more about the area of the rectangle here;

https://brainly.com/question/14383947

Ginger is solving for 'x' in a quadratic equation to find the amounts by which the length and width of the original 9 ft by 6 ft patio must be increased to achieve an area of 88 sq ft.

The student is working on a quadratic equation derived from the area of a rectangle. The original dimensions of the patio are 9 ft by 6 ft, which, when both the length and width are increased by the same amount 'x', the new area becomes 88 sq ft. Ginger is thus solving the equation (6 + x)(9 + x) = 88 using the zero product property.

By expanding this, we get a quadratic equation in the form of x^2 + 15x + 54 = 88, which can be simplified to x^2 + 15x - 34 = 0. The zeros of this function will give us the values of 'x' where the new dimensions of the patio result in an area of 88 sq ft. Consequently, the solutions 'x' are the amounts by which the length and width of the original patio would need to be increased to reach the new area.

[tex]\bf y=\stackrel{\stackrel{m}{\downarrow }}{-2}x+\stackrel{\stackrel{y}{\downarrow }}{4}\qquad \impliedby \qquad \begin{array}{|c|ll} \cline{1-1} slope-intercept~form\\ \cline{1-1} \\ y=\underset{y-intercept}{\stackrel{slope\qquad }{\stackrel{\downarrow }{m}x+\underset{\uparrow }{b}}} \\\\ \cline{1-1} \end{array}[/tex]

The equation of the line in slope-intercept form of a line with slope –2 and y-intercept 4 is y = -2x + 4.

The ratio that y increase as x increases is the slope of a line. The slope of a line reflects how steep it is, but how much y increases as x increases. Anywhere on the line, the slope stays unchanged (the same).

[tex]\rm m =\dfrac{y_2-y_1}{x_2-x_1}m=(y₂-y₁) / (x₂-x₁)[/tex]

It is given that:

A line with slope –2 and y-intercept 4.

The linear equation in one variable can be made:

As we know,

The standard equation of the line is:

y = mx + c

Here m is the slope and c is the y-intercept.

m = -2

c = 4

y = -2x + 4

Thus, the equation of the line in slope-intercept form of a line with slope –2 and y-intercept 4 is y = -2x + 4.

Learn more about the slope here:

brainly.com/question/3605446

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Answer:

the first one

Step-by-step explanation:

Complex numbers emerge when you take the square root of a negative number, since the imaginary unit [tex]i[/tex] is defined by the relation [tex]i^2=-1[/tex], which implies [tex]\sqrt{-1}=i[/tex]

The only option involving the square root of a negative number is the last one.

Answer:

option D

Step-by-step explanation:

Complex number is a number that has negative under the square root.

Square root (-1) =i is a complex number

square root of a negative number is a complex.

First option does not have any negative number under the square root so it is not a complex.

second option also not have negative number under square root . So it is not a complex

third option have positive 7 under the square root so it is not a complex

Fourth option have -9/5 under the square root . So it is a complex number

Answer: Second option.

Step-by-step explanation:

Below are some transformation for a function f(x):

If [tex]f(x)+k[/tex] then the function is shifted up "k" units.

If [tex]f(x)-k[/tex] then the function is shifted down "k" units.

If [tex]f(x+k)[/tex] then the function is shifted "k" units to the left.

If [tex]f(x-k)[/tex] then the function is shifted "k" units to the right.

Knowing this tranformations and given the parent function [tex]f(x)=x^3[/tex] and the function [tex]g(x) = (x -2)^3 + 7[/tex], we can conclude that the function g(x) is shifted 2 units to the right and 7 units up.

We can observe that this matches with the second option.

Answer:

1. 264 ft/s

2. 5280 feet

Step-by-step explanation:

Changing miles per seconds to feet per hour

If 1 mile= 5280 feet

180 miles=?

[tex](180*5280)/1 = 950400[/tex]

=950400 feet

1 hour= 60×60 seconds = 3600

180 miles/hour = feet/sec = 950400/3600 =264 ft/s

To find the number of feet the parachutist fall during 20 seconds;

Distance= speed × time

              =264×20 = 5280 feet

Answer:

[tex]\large\boxed{S.A.=96\ cm^2}[/tex]

Step-by-step explanation:

We have:

(1) two trapezoids with bases b₁ = 7cm and b₂ = 5cm and the height h = 4cm

(2) three rectangles 3 cm × 7 cm, 3 cm × 4 cm and 3 cm × 5 cm.

The formula of an area of a trapezoid:

[tex]A=\dfrac{b_1+b_2}{2}\cdot h[/tex]

Substitute:

[tex]A=\dfrac{7+5}{2}\cdot4=24\ cm^2[/tex]

Calculate the areas of the rectangles:

[tex]A_1=(3)(7)=21\ cm^2\\\\A_2=(3)(4)=12\ cm^2\\\\A_3=(3)(5)=15\ cm^2[/tex]

The Surface Area:

[tex]S.A.=(2)(24)+21+12+15=96\ cm^2[/tex]

Answer:

the angle of depression is 45 degrees

Step-by-step explanation:

120(150)

angle theorem

points postulate

90/2=45

please mark brainliest and give thanks

y - 6 = -(x + 3) and y + 2 = - (x - 5).

The line AB passes through the points A(-3, 6) and B(5, -2). Find the point-slope form.

First, we have to calculate the slope using the equation m = (y₂ - y₁)/(x₂ - x₁):

    x, y

A(-3, 6)

B( 5,-2)

m = [-2 - (6)]/[5 - (-3)] = (-2 - 6)/(5 + 3)

m = -8/8

m= -1

Writing the point-slope form equation as (y - y₁) = m (x - x₁), with A(-3, 6):

y - 6 = -1[(x -(-3)]

y - 6 = - (x + 3)

Writing the point-slope form equation as (y - y₁) = m (x - x₁), with B(5, -2):

y - (-2) = - (x - 5)

y + 2 = - (x - 5)

Answer:

[tex]g(x)= 3x-2[/tex], graph shifted 2 units down.

Step-by-step explanation:

[tex]g(x)= 3x-2[/tex]

g(x) = 3x is a parent function.

When we compare the graph of parent function g(x)= 3x with [tex]g(x)= 3x-2[/tex], negative 2 is added at the end

f(x)---> f(x) + a , the graph will be shifted 'a' units up

f(x)-> f(x) -a , the graph will be shifted 'a' units down

[tex]g(x)= 3x-2[/tex], In this g(x) we have -2 at the end.

So the graph will be shifted 2 units down.

The graph of 3x - 2 is a vertical translation by 2 units down of the function f(x) = 3x

According to the question, we are given the parent function f(x) = 3x, we need to determine the relationship between the parent function and g(x) = 3x - 2

If the function f(x) translate by k units downwards, the resutlting function will be expressed as h(x) - k.

Hence if h(x) = 3x translate by 2 units downwards, the resulting function will be expressed as 3x - 2.

The graph of 3x - 2 is a vertical translation by 2 units down of the function h(x) = 3x

Learn more on translation here: https://brainly.com/question/12861087

Answer:

W =2.6816

Step-by-step explanation:

Is means equals and of means multiply

W = 8% * 33.52

Change to decimal form

W = .08 * 33.52

W =2.6816

45x = 25x + 57 + x

45x = 26x + 57

45x - 26x = 57

19x = 57

x = 57/19

x = 3

Answer:

9

Step-by-step explanation:

for the expression y(x+x)+3, we can first simplify:

y(2x)+3

then we can substitute 1 for x and 3 for y:

3(2*1)+3

multiply inside the parenthesis:

3*2+3

multiply 3 and 2:

6+3

add 3:

9

Therefore, this evaluates to 9

y( x + x) + 3, where x = 1 and y=3

Plug 1 in for x and 3 in for y like...

3( 1 + 1) + 3

To evaluate apply the rules of PEMDAS (Parentheses, Exponent, Multiplication, Division, Addition, Subtraction)

Parentheses

3( 1 + 1) + 3

3(2) + 3

Exponent

There are none so go on to the next step

Multiplication

3(2) + 3

6 + 3

Division

There are none so go on to the next step

Addition

6 + 3

9

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The answer is d.

Step-by-step explanation:

As we know, sin x= cos (90°-x)

sin 18° = cos (90°-18°)

= cos 72°.

Similarly, sin 72°= cos (90°-72°)

= cos 18°

But, sin 55°= cos (90°-55°)

= cos 35°

Answer:A

Step-by-step explanation:

The formula is 2pir, so you divide by the 2, the pin the pi, then you have the radius, r.

[tex]\bf ~~~~~~\textit{parabola vertex form} \\\\ \begin{array}{llll} \stackrel{\textit{we'll use this one}}{y=a(x- h)^2+ k}\\\\ x=a(y- k)^2+ h \end{array} \qquad\qquad vertex~~(\stackrel{}{ h},\stackrel{}{ k}) \\\\[-0.35em] ~\dotfill\\\\ f(x)=-2(x+4)^2-3\implies f(x)=-2[x-(\stackrel{h}{-4})]^2\stackrel{k}{-3}~\hfill \stackrel{vertex}{(-4,-3)}[/tex]

well, to get a second point, we simply pick a random "x" hmmm  say x = 1, so then

f( 1 ) = -2( 1 + 4) ² - 3

f( 1 ) = -2(25) - 3

f( 1 ) = -53

so from that we get the point of x = 1, y = -53   ( 1 , -53), so it looks like the picture below.

Answer:

A)3

Step-by-step explanation: