d) The surface area if Lake Superior is approximately 31,700 square miles. Express
the surface area of the lake in square kilometers to the nearest square kilometer.
Use the fact that 1 kilometer = 0.6214 miles. (5 pt.)

Answer:

n² + 3

Step-by-step explanation:

It's a quadratic sequence, so it follows the form:

y = ax² + bx + c

We're given five points that satisfy the equation.  (1, 4), (2, 7), (3, 12), (4, 19), and (5, 28).  Picking any three points, we can form a system of equations.

If we pick (1, 4), (2, 7), and (4, 19):

4 = a(1)² + b(1) + c

7 = a(2)² + b(2) + c

19 = a(4)² + b(4) + c

4 = a + b + c

7 = 4a + 2b + c

19 = 16a + 4b + c

Through substitution, elimination, or trial and error, we can find a = 1, b = 0, and c = 3.

y = x² + 3

So the nth term of the sequence is n² + 3.

Answer:

a(n) = a(n-1) + (2n - 1)

Step-by-step explanation:

Start by analyzing the pattern:

7 is 3 more than 4;

12 is 5 more than 7;

19 is 7 more than 12, and so on.  

Each step is an odd number and is 2 greater than the previous step.

a(2) = 7 = 4 + step = 4 + 3 = 7

a(3) = 12 = 7 + step = 7 + 5 = 12

a(4) =                      12 + 7  = 19

a(5) =                       19 + 9 = 28

and so on.  

Looking at a(2), we see that the step is 2+1, or 3;

Looking at a(3), we see that the step is 2(3) - 1, or 5;

Looking at a(4), we see that the step is 2(4) - 1, or 7; and so on.

Looking at a(n), we see that the step is 2n - 1.

Thus, a(n) = a(n-1) + (2n - 1)

Answer:

The length of the missing side of the triangle is represented by the equation:

  (6a + 2b - 5) - (2a - 3b) - (a - 3)

= 6a + 2b - 5 - 2a + 3b - a + 3

= 3a + 5b - 2

Answer:

Step-by-step explanation:

x + 3y = 28

Put x = 28 and solve for y:

28 + 3y = 28           subtract 28 from both sides

28 - 28 + 3y = 28 - 28

3y = 0          divide both sides by 3

3y : 3 = 0 : 3

y = 0

The expression can be simplified to [tex]625 \times (uv)^4.[/tex]

To rewrite the expression (-5uv)(-5uv)(-5uv)(-5uv) using the properties of exponents, you can consolidate it using the exponent rule that states when you multiply numbers with the same base, you add the exponents. In this case, the base is -5uv, and you are multiplying it four times, so the exponent is 4:

[tex](-5uv)(-5uv)(-5uv)(-5uv) = (-5uv)^4[/tex]

Now, you can simplify further by applying the rule for raising a power to a power, which states that when you raise an exponentiated term to another exponent, you multiply the exponents:

[tex](-5uv)^4 = -5^4 \times (uv)^4[/tex]

-5^4 means -5 multiplied by itself four times:

[tex]-5^4 = -5 \times -5 \times -5 \times -5 = 625[/tex]

So, the expression can be simplified to:

[tex]625 \times (uv)^4[/tex]

This is the expression rewritten using the properties of exponents.

for such more question on expression

https://brainly.com/question/1859113

#SPJ2

Answer:

C

Step-by-step explanation:

To evaluate f(g(7)), substitute x = 7 into g(x), then substitute the result into f(x)

g(7) = (2 × 7) - 5 = 14 - 5 = 9, then

f(9) = 3(9)² - 4 = 243 - 4 = 239 → C

Option C is correct.

Given functions are, [tex]f(x)=3x^{2} -4,g(x)=2x-5[/tex]

We have to find  [tex]f(g(7))[/tex].

             [tex]g(7)=2*7-5=14-5=9[/tex]

So that,  [tex]f(g(7))=f(9)[/tex]

           [tex]f(9)=3*(9)^{2}-4\\ \\f(9)=243-4=239\\\\f(g(7))=f(9)=239[/tex]

Learn more about the composite function here:

https://brainly.com/question/10687170

Answer:

y = (-1/2)x -3

Step-by-step explanation:

We are given

y = 2x-17

which is in slope-intercept form: y = mx +b

Where m is the slope. so, m= 2

But this is perpendicular, When a line is perpendicular then the slope become -1/m so in our case the slope m will be = -1/2

Using the point(-8,1) we can find the b i.e the y intercept

We have x = -8, y =1 and m=-1/2

y = mx + b

1 = (-1/2)(-8) + b

1 = 4 + b

=> b = 1-4

b = -3

The equation of slope intercept form will be

y = mx + b

Putting value of m= -1/2 and b = -3

y = (-1/2)x -3

[tex]\text{Hey there!}[/tex]

[tex]\text{The word \bf{of}}\text{ means multiply in mathematical terms.}[/tex]

[tex]\text{Percentages (\%) usually run out of 100}[/tex]

[tex]\text{First, put the numbers set to multiply from each other.}[/tex]

[tex]\text{7\%}\times\text{14.50}[/tex]

[tex]\text{(You can convert the percentage into a decimal (if you want but it is mandatory)}[/tex] [tex]\leftarrow\text{in order for you to convert them into a decimal you have to divide 7\%}[/tex] [tex]\text{from 100}[/tex]

[tex]\dfrac{7\%}{100}[/tex]

[tex]\dfrac{7\%}{100}=0.07[/tex]

[tex]\text{Next, solve for your answer.}[/tex]

[tex]\text{0.07}\times\text{14.50 = ?}[/tex]

[tex]\text{Solve the one above, and you SHOULD get your result!}[/tex]

[tex]\boxed{\boxed{\bf{Thus,\ your\ answer\ is: 1.015}}}\checkmark[/tex]

[tex]\text{Good luck on your assignment and enjoy your day!}[/tex]

~[tex]\frak{LoveYourselfFirst:)}[/tex]

Answer:

True options:

[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]

Side Q'S' lies on a line with a slope of -1.

The distance from Q' to the origin is twice the distance from Q to the origin.

Step-by-step explanation:

Triangle QRS is dilated according to the rule [tex]D_{O,2} (x,y).[/tex] This dilation has the rule

[tex](x,y)\rightarrow (2x,2y)[/tex]

So,

[tex]S(-1,1)\rightarrow S'(-2,2)\\ \\Q(-3,3)\rightarrow Q'(-6,6)\\ \\R(2,4)\rightarrow R'(4,8)[/tex]

True options:

[tex]D_{O,2} (x,y) = (2x, 2y)[/tex]

Side Q'S' lies on a line with a slope of -1.

The distance from Q' to the origin is twice the distance from Q to the origin.

False options:

QR is longer than Q'R', because QR is twice shorter than Q'R'.

The vertices of the image are closer to the origin than those of the pre-image, because the vertices of the per-image are closer to the origin than those of the image (see attached diagram).

Answer:

1, 2, 5 on Ed

Step-by-step explanation:

Answer:

The correct answer is R(2, 4)

Step-by-step explanation:

Answer:

y+3 = -7/5(x+2)

Step-by-step explanation:

First we need to find the slope

m = (y2-y1)/(x2-x1)

   = (4--3)/(-7--2)

  = (4+3)/(-7+2)

  =7/-5

  = -7/5

The point slope form is y-y1 = m(x-x1)

y--3 = -7/5(x--2)

y+3 = -7/5(x+2)

We could use the second set of points

y-4 = -7/5(x--7)

y-4 =-7/5(x+7)

For this case we have that by definition, the distance between two points is given by:

[tex]d = \sqrt {(x_ {2} -x_ {1}) ^ 2+ (y_ {2} -y_ {1}) ^ 2}[/tex]

We have the following points:

[tex](x_ {1}, y_ {1}): (- 3,4)\\(x_ {2}, y_ {2}) :( 21,11)[/tex]

We replace:

[tex]d = \sqrt {(21 - (- 3)) ^ 2+ (11-4) ^ 2}\\d = \sqrt {(21 + 3) ^ 2 + (11-4) ^ 2}\\d = \sqrt {(24) ^ 2 + (7) ^ 2}\\d = \sqrt {576 + 49}\\d = \sqrt {625}\\d = 25[/tex]

Thus, the distance between the two points is 25 units.

Answer:

25

Answer:

The distance is 25 units

Step-by-step explanation:

Points to remember

Distance formula

Length of a line segment with end points (x1, y1) and (x2, y2) is given by,

Distance = √[(x2 - x1)² + (y2 - y1)²]

To find the distance between given points

Here (x1, y1) = (-3, 4) and (x2, y2) = (21, 11)

Distance = √[(x2 - x1)² + (y2 - y1)²]

= √[(21 - -3)² + (11 - 4)²]

= √[(21 +3)² + (11 - 4)²]

= √[24² + 7²]

 = √(576 + 49)

 = √625

 =25

Therefore the distance is 25 units

Answer:

The resulting equation is

x^2/4+16x^2/9=1

Step-by-step explanation:

The given equations are:

3y=12x   eq(1)

x^2/4+y^2/9=1    eq(2)

We need to isolate variable y in equation 1

Divide both sides of the equation with 3

3y/3 = 12x/3

y = 4x

Now, substitute the value of y=4x in second equation

x^2/4+y^2/9=1

x^2/4 + (4x)^2/9 = 1

The resulting equation is

x^2/4+16x^2/9=1

Answer:

[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]

Step-by-step explanation:

Given system of equations,

[tex]3y=12x-----(1)[/tex]

[tex]\frac{x^2}{4}+\frac{y^2}{9}=1----(2)[/tex]

As per statement,

Isolating the variable y in the first equation,

[tex]y=\frac{12}{3}x=4[/tex]

Now, substituting into the second equation,

[tex]\frac{x^2}{4}+\frac{(4x)^2}{9}=1[/tex]

Which is the resulting equation,

Simplifying the equation,

[tex]\frac{x^2}{4}+\frac{16x^2}{9}=1[/tex]

[tex]\frac{9x^2+64x^2}{36}=1[/tex]

[tex]73x^2=36[/tex]

Answer:

5

Step-by-step explanation:

When you given input of "x" into a floor function  y = ⌊x⌋ , it gives as output the "greatest integer less than or equal to x"

For example, if we were to given 1.4 as the input for floor function, it will return the greatest integer that is less than or equal to 1.4, so it would be 1.

So, if we put 5.7 into this function, the floor function would give "5" as the output.

Thus value of y would be 5

Answer:

5

Step-by-step explanation:

Answer:

The scale factor is equal to 1/2

The dimensions of each channel when splits the screen is 46 in x 38 in

Step-by-step explanation:

we know that

The dimensions of the new television is 92 in x 76 in

Remember that

If two figures are similar, then the ratio of its areas is equal to the scale factor squared

Let

A1 -----> the area of the new television

A2 ----> the area of each channel when splits the screen

z-----> the scale factor

[tex]z^{2} =\frac{A2}{A1}[/tex]

we have that

The area of the new television is 4 times the area of each channel

[tex]A1=4A2[/tex]

[tex](A2/A1)=1/4[/tex]

[tex]z^{2} =\frac{1}{4}[/tex]

[tex]z=\frac{1}{2}[/tex] -----> the scale factor

so

When splits the screen, the dimension of each channel is equal to

92/2 in x 76/2 in

so

46 in x 38 in

Remember, if two figures are similar then the scale factor is equal to the ratio of their corresponding sides

Verify the value of the scale factor

92/46=1/2

or

76/38=1/2

See the attached picture:

Answer:

Step-by-step explanation:

Compare y = (1/2)x - 3 and y = (-1/2)x - 3.

They have different slopes but the same y-intercept (0, -3).  Eliminate the first answer choice.

They have different slopes.  Eliminate the second answer choice.

Their graphs intersect, so they have a solution.  Eliminate the third choice.

They have different slopes but the same intercept, so they have one solution.  The fourth answer choice is the correct one.

Answer:

the fourth one is the corect one

Step-by-step explanation:

the fourth one is the corect one because i did the mathand i checked it twice and its right and also i asked my friend and he said it the fourth one

hope that helps you

Answer:

dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]

Step-by-step explanation:

* Lets revise some rules for the derivative

- The derivative of ㏑(f(x)) = 1/f(x) × f'(x)

- The derivative of u/v = (vu'-uv')/v²

- The derivative of the constant is 0

* Lets solve the problem

∵ y = ㏑[(4x³ - 7)/(3x^5 + 1)]

- Let u = 4x³ - 7 and v = 3x^5 + 1

∵ u = 4x³ - 7

∴ u' = 4(3)x^(3-1) - 0 = 12x²

∵ v = 3x^5 + 1

∴ v' = 3(5)x^(5-1) + 0 = 15x^4

∵ The derivative of u/v = (vu' - uv')/v²

∴ The derivative of u/v = [tex]\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)^{2}}[/tex]

∵ The derivative of ㏑(f(x)) = 1/f(x) × f'(x)

∴ dy/dx = [tex]\frac{1}{\frac{(4x^{3}-7)}{(3x^{5}+1)}}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4}}{(3x^{5}+1)^{2}}][/tex]

- Simplify by cancel bracket (3x^5 + 1)from the 1st fraction with the

 same bracket in the 2nd fraction

∴ dy/dx = [tex]\frac{1}{(4x^{3}-7)}*[\frac{(3x^{5}+1)(12x^{2})-(4x^{3}-7)(15x^{4})}{(3x^{5}+1)}][/tex]

Answer:

Step-by-step explanation:

The dominant term of this function is x^4.  The graph of x^4 starts in Quadrant II and continues in Quadrant I.

If we have y = -x^4, the graph starts in Quadrant III and continues in Quadrant IV.  This is the end behavior for f(x)=-x^4+5x^3-3.

Answer:

x = -8  &  x = 3

Step-by-step explanation:

Vertical asymptote occur when denominator is 0.

So to find the x-values, we need to middle term factor the denominator. Shown below:

[tex]x^2+5x-24\\=(x+8)(x-3)\\x=3, -8[/tex]

Thus, at x = 3 and at x = -8  --  there is vertical asymptote.

Answer:

[tex]x^{5}[/tex]

Step-by-step explanation:

We simply add the exponents together. This depicts the exponent product rule, which states that when multiplying together two values with the same base (x) but different exponents, we can solve the answer by adding together the exponents with the base staying the same.

Explanation / Proof:

[tex]2^{2} * 2^{3} = 4 * 8 = 32\\\\2^{2} * 2^{3} = 2^{5} = 2*2*2*2*2 = 32[/tex]

As you can see, adding together the exponents will give the same answer. Therefore, the answer is [tex]x^{5}[/tex].

Answer for A. (-8,-2)

answer for B. (4,-7)

Answer:

y = 4.125x + 496.25

Step-by-step explanation:

Set the data up as points. Then deal with the points.

Givens

(30,620)

(70,785)

y2 = 785

y1 = 620

x2 = 70

x1 = 30

Formula

Slope = (y2 - y1) / (x2 - x1)

Solution

Slope = (785 - 620)/(70 - 30)

Slope = 165 / 40

Slope = 4.125

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

Now you need the y intercept. Either one of the two given points will give you that.

y = 620

x = 30

m = 4.125

y = mx + b

620 = 4.125*30 + b

620 = 123.75 + b

620 - 123.75 + b

b = 496.25

the linear function that describes the relationship between study hours and exam scores is:

y = 4.125x + 496.25

To find a linear function that fits the data provided, we'll use the points (30, 620) and (70, 785), which represent the number of hours spent studying and the corresponding exam scores. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept.

First, we calculate the slope (m):

m = (y2 - y1) / (x2 - x1) = (785 - 620) / (70 - 30) = 165 / 40 = 4.125

Next, we use one of the points to solve for b (y-intercept). Let's use the point (30, 620):

620 = 4.125(30) + b

b = 620 - (4.125 × 30) = 620 - 123.75 = 496.25

So the linear function that describes the relationship between study hours and exam scores is:

y = 4.125x + 496.25

Answer: ≈ 1.414

Step-by-step explanation:

You can use the pythagorean theorem, a^2 + b^2 = c^2

a^2 and b^2 are the legs and c^2 is the hypotenuse.

1^2 + 1^2 = c^2

1 + 1 = c^2

2 = c^2

√ 2 = √ c^2

c = ≈ 1.414

Answer:

-a (14 +a) =0

Step-by-step explanation:

-14a-a^2=0

Factor out  -a

-a (14 +a) =0

Using the zero product property

-a =0   14+a =0

a =0   a = -14

Answer:

2 units

Step-by-step explanation:

ok, so, the line below says HJ is (x+1) units long. therefore:

2x-16+8 = x+1

now, let's isolate the variable.

2x-x = 1+16-8

x = 9

since we now defined variable x, we can add it to the equation that determines the length of HI.

2x-16

2(9)-16

18-16

2

the length of line segment HI is 2 units

hope this helped!

HI + IJ = HJ

With this knowledge you can from an equation like so...

2x - 16 + 8 = x + 1

Now combine like terms and solve for x

2x + (- 8 + 8) = x + 1 + 8

2x = x + 9

2x - x = x - x + 9

x = 9

To find HI plug 9 in for x and simplify

2(9) - 16

18 - 16

2

The length of HI is 2!!!

Hope this helped!

~Just a girl in love with Shawn Mendes

Answer:

The answer is 25

Step-by-step explanation:

Answer:

m=4

Step-by-step explanation:

3-(-1)/-1-(-2)=3+1/-1+2=4/1

Answer:

4

Step-by-step explanation:

Slope formula:

     ↓

[tex]\frac{\huge Y_2-Y_1}{\huge X_2-X_1}=\frac{Rise}{run}[/tex]

[tex]Y_2=(-1)\\Y_1=3\\X_2=(-2)\\X_1=(-1)\\[/tex]

[tex]\frac{(-1)-3}{(-2)-(-1)}=\frac{-4}{-1}=4[/tex]

Therefore, the slope is 4.

4 is the correct answer.

I hope this helps you, and have a wonderful day!

Find  the cost of the chair and desk by multiplying the total amount pent by the 70%

Chair and desk = 900 x 0.70 = $60

Subtract that cost from the total spent:

900 - 630 = $270 was spent on the other three items.

Subtract the cost of the bookshelf:

270 - 50 = 220

The two tables cost 220.

For the price of one table divide that cost by 2:

220/2 = 110

One table cost $110.

The cost of each table is $110.

Given that

There are five items i.e. chair, bookshelf, 2 tables, and a desk.

The total amount incurred for these 5 items should be $900.

And, the chair + desk = 70% of total.

The cost of the bookshelf is $50.

Since 70% of total = chair + desk

That means

Chair + desk = 0.70 of $900 = $630

So the other items cost should be

= $900 - $630

= $270

And, the cost of bookshelf is $50

So, the two tables cost should be

= $270 - $50

= $220

So for one it should be

= $220 ÷ 2

= $110

Therefore we can conclude that the cost of each table is $110.

Learn more about the cost here: brainly.com/question/5282141

Answer:

5.6b + 3.4a

Step-by-step explanation:

Simply evaluate be match each term with its corresponding variable, and watch out for where you have to distribute negatives, meaning that you have a couple of double negatives in there.

Double Negative = Positive

Answer:

it’s C and E

Step-by-step explanation:

Answer:

C D and E

Step-by-step explanation:

The only one you probably can never do is B. It get's you no where. The way A is written, it is not much help to write 18 in base 2. So A and B both won't work. The common logs and the natural logs will both work

Log(4^(x + 3)) = Log(18)

(x + 3) Log(4) = log (18)

(x + 3) * 0.6021 = 1.2553

x + 3 = 1.2553/0.6021

x + 3 = 2.08496

Now all you need do is subtract 3 from both sides. The natural logs will give you the same answer.

You could take base-4 logs of both sides and it is a possible first step, but d and e are much more efficient. You have to change both sides to base 4 before you can proceed. This one is kind of iffy.  It does say possible first steps.

Answer:

C.Take the base-4 logarithm of each side.

D.Take the natural logarithm of each side.

E. Take the common logarithm of each side.

Step-by-step explanation: