What is the length of AP?

[tex]\lim \limits_{x \to \infty} \sqrt{x^2 +x(2a+2b) +4ab-x}\\\\\\=\lim \limits_{x \to \infty} \sqrt{x^2 \left( 1 + \dfrac{2a+2b}{x}+ \dfrac{4ab}{x^2} - \dfrac 1{x} \right)}\\\\\\=\sqrt{\lim \limits_{x \to \infty} x^2 \cdot \lim \limits_{x \to \infty} \left( 1 + \dfrac{2a+2b}{x}+ \dfrac{4ab}{x^2} - \dfrac 1{x} \right)}}\\\\\\=\sqrt{ \infty \cdot (1+0+0-0)}\\\\=\sqrt{ \infty \cdot 1}\\\\=\infty[/tex]

Answer:

$134.89.

Step-by-step explanation:

Monthly interest = 0.06/12 and its for 5*12 months.

Amount after 5 years = 100(1 + 0.06/12)^(5*12)

= 100(1 + 0.06/12)^60

= $134.89

Answer:

4/663.

Step-by-step explanation:

There are  4 aces and 4 2's in a pack of cards.

Prob(First drawing an Ace) = 4/52 = 1/13.

After drawing this card there are now 51 cards left, so:

Prob(Next drawing a 2) = 4/51.

Required probability

= 1/13 * 4/51

=  4/663

Answer:

First, we need to keep in mind that there are 52 cards in a deck.
Second, we need the probability of getting an ace.
[tex]\frac{4}{52\\}[/tex] = [tex]\frac{1}{13}[/tex]
Now that that card is taken out of the deck, we need to subtract that card from the total amount of cards. Now there will be 51 cards.
Next, we need to find the probability of getting a 2. Like the Ace, there 4 of them.
So,
[tex]\frac{4}{51}[/tex]
Now, we multiply both of the probabilities.
[tex]\frac{1}{13} * \frac{4}{51} = \frac{4}{663}[/tex]

Since we cannot Reduce, There is your answer!

[tex]\frac{4}{663}[/tex]

∫Maybe·Kuro∫

The equation of the line passing through these two points (1, 2) and (3, 8) will be y  = 3x – 1. Then the correct option is C.

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

The points are (1, 2) and (3, 8).

Then the equation of the line passing through these two points (1, 2) and (3, 8) will be

[tex]\rm (y - 2) = \dfrac{ 8- 2}{3-1} (x - 1)[/tex]

On simplifying the equation, we have

y - 2 = 3(x – 1)

y - 2 = 3x – 3

   y  = 3x – 1

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Answer: 37 students in the class

Step-by-step explanation:

Let n = number of books,

Let s = number of students

We get the following expressions:

n = 3s + 17

4 = [tex]\frac{n}{s-5}[/tex]

Solve this system using substitution:

[tex]4=\frac{3s+17}{s-5}[/tex]

[tex]4(s-5) = \frac{3s+17}{s-5} (s-5)[/tex]

[tex]4s -20 = 3s+17\\[/tex]

[tex]s-37 = 0\\[/tex]

[tex]s=37[/tex]

Answer: Solution- (10,4)

Step-by-step explanation:

x-2y=2   x-y=6              x-2(4)=2

-1(x-y=6)                        x-8=2

-x+y=-6                         +8  +8

                                      x=10

x-2y=2                            

-x+y=-6                           10-2(4)=2

-y=-4                                10-8=2

-1   -1                                  2=2

y=4

Answer:

y= -3/2x - 3/2

Step-by-step explanation:

So you know the gradient of the line is -3/2x since that is the gradient.

So the equation so far is y=-3/2x +c

Then, substitute the co-ordinates to find c so:

-3 = -3/2 +c

-3/2 = c

The equation is y = -3/2x -3/2

Answer:

I don't know F but if y'all do let me now.

Step-by-step explanation:

(b) the price in the very middle of a data set, with exactly half of the houses priced for less and half priced for more.

(c) The mode is the value that appears most frequently in a data set. A set of data may have one mode, more than one mode, or no mode at all. Other popular measures of central tendency include the mean, or the average of a set, and the median, the middle value in a set.

(d) The two biggest things that come to mind right away is how is it going to be used and who is going to be using it? While we would all love to get the highest quality that’s just not always possible. So, that’s a good starting point for me is considering the answer to those two questions.

(e) Price and other details may vary based on product size and color.

The difference between the most and least expensive lamps represented on the stem and leaf plot is 66.

The stem and leaf plot that completes the question is added as an attachment.

The median cost is the leaf element at the middle.

The plot has 18 leaves.

So, the median position is:

Median = (18 + 1)/2 = 9.5th

This means that the median is the mean of the 9th and the 10th items.

So, we have:

Median = (58 + 58)/2

Median = 58

Hence, the median cost is $58

This is the element with the highest frequency in the plot.

From the attached plot 65 has the highest frequency of 3

Hence, the modal cost is 65

From the plot, we have:

Most expensive = 78

Least expensive = 12

The difference (d) is:

d = 78 - 12

d = 66

Hence, the difference between the most and least expensive lamps is 66.

This means that we check the items in the range 20 to 40 (exclusive)

The elements in this range are:

25, 28, 30, 32 and  34

Hence, 5 lamps that cost more than $20 but less than $40

From the plot, we have:

Less than $40 =  6

More than $40 =  12

The ratio is represented as:

Ratio = 6 : 12

Simplify

Ratio = 1 : 2

Hence, the ratio of lamps that cost less than $40 to more than $40 is 1 : 2

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Answer:

use The Law of Cosines first to calculate the largest angle. then use The Law of Sines to find another angle. and finally, use the angles of a triangle add to 180° to find the last angle.

Step-by-step explanation:

The scalene triangle is a type of triangle with sides of three different lengths and angles of three different measurements. In every scalene triangle, the shortest side is opposite the smallest angle and the longest side is opposite the largest angle.

Answer:

The 6 is in the ten-thousands place

Step-by-step explanation:

6 written as a ten-thousand is 60,000

A solid line passes through (-1, 0) and (0, 3). The area to the left of the line is shaded gray.

Here we have the inequality:

3y - 9x ≥ 9

First, we should isolate y on one side of the inequality.

3y  ≥ 9x + 9

y  ≥ 3x + 3

Then, the graph will be a solid line of the form:

y =  3x + 3

Where the line is solid because the points on the line are solutions, and we need to shade all the region above the line.

Also, notice that for the line:

y = 3x + 3

if x = -1 we have:

y = 3*(-1) + 3 = 0

if x = 0 we have:

y = 3*0 + 3 = 3

Then the line passes through (0, 3) and (-1, 0). So the correct option is the second one.

"Number graph ranging from negative ten to ten on the x and y axes. A solid line passes through (negative one, zero) and (zero, three). The area to the left of the line is shaded gray."

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Using a proportional relationship, it is found that when x = -7, the value of y will be of y = 6.

A proportional relationship is a function in which the output variable is given by the input variable multiplied by a constant of proportionality, that is:

y = kx

In which k is the constant of proportionality.

When y varies inversely with x, the rule is given by:

[tex]y = \frac{k}{x}[/tex]

y = −3 when x = 14, hence we use this to find k.

[tex]-3 = \frac{k}{14} \rightarrow k = -42[/tex]

Then:

[tex]y = -\frac{42}{x}[/tex]

Then when x = -7, y = -42/-7 = 6.

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Answer:

36

Step-by-step explanation:

You multiply354 and 16 then divide

Answer:

r = -7

Step-by-step explanation:

-4 + 2r - 5r = 17

=> 2r - 5r = 17 + 4

=> -3r = 21

=> r = 21/(-3)

=> r = -7

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The account balance after a period of 5 years will be $1.63634×10²⁰.

Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.

[tex]A = P(1 + \frac{r}{n})^{nt}[/tex]

A = final amount

P = initial principal balance

r = interest rate

n = number of times interest applied per time period

t = number of time periods elapsed

Given the principal amount is $12,385, the rate of interest is 7.5%, and the time period is daily. Therefore, the amount can be written as,

[tex]A = P(1 + \frac{r}{n})^{nt}\\\\A = \$12,385(1 + \frac{7.5}{365})^{(365 \times 5)}\\\\A = \$1.63634 \times 10^{20}[/tex]

Hence, the account balance after a period of 5 years will be $1.63634×10²⁰.

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Answer:

Step-by-step explanation:

Area of rectangle is  b*h

so

a = (x-3)(x+7)

75 = (x-3)(x+7)

75 = x²+4x-21

0 = x²+4x-96

(x+12)(x-8)=0

x = -12, or x = 8

Answer:

  $37,500

Step-by-step explanation:

The amount of the fee is the product of the fee rate and the amount to which that rate is applied.

__

  3.75% × $1,000,000 = 0.0375 × $1,000,000 = 37.5 × $1000

  = $37,500

The fee on a $1M loan could range up to $37,500.

_____

Additional comment

If you're computing this by hand, it can be easier to (a) use scientific notation, or (b) adjust the decimal points as we have shown here. In this case, we multiplied the percentage by 1000 and divided the loan amount by 1000. The product remains the same, but the numbers are easier to deal with.

In scientific notation, this is 3.75E-2 × 1E6 = 3.75E4 = 37.5E3 = 37,500, where the "E" notation would be that used by a calculator or spreadsheet.

Answer:

672 litres.

Step-by-step explanation:

Convert the measurements to cm:

14 m = 1400 cm

The capacity = 1400 * 8 * 60

= 672,00 cm^3

There are 1000 cm^3 in 1 litre so the answer is

672 litres.

Answer:

69500

Step-by-step explanation:

[tex]\frac{695000}{x}=\frac{100\%}{10\%}\\\frac{x}{695000}=\frac{10}{100}\\\Rightarrow x=69500[/tex]

Answer:

The range of the function is [0 , ∞) ⇒ answer B. Step-by-step explanation: * lets revise the meaning of the domain and the range - The domain is the values of x - The domain is all the values of x which make the function is defined - If there are some values of x make the function undefined, we exclude these values from the domain

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

10=7-m

m=???

so if you do 10+7 which equal 17 and then do 17-7 you will get ten

m=17

have a good day

Answer:

the answer is -3

Step-by-step explanation:

10 = 7 -m

swap sides so that all the variable terms are on the left hand side

7 - m =10
subtract 7 from both sides

-m + 10 - 7

subtract 7 from 10 to get 3

multiply both sides by -1

m = -3

Answer: D (bottom option)

Axis of Symmetry: x = -8

Vertex: (-8, -40)

Y-Intercept: 24

Step-by-step explanation:

Start by putting the equation into vertex form, which you can do by completing the square. This means the equation will in the form [tex]y=a(x-h)^2+k[/tex].

Once you've done that, you'll get [tex]y=(x+8)^2-40[/tex]. This means that h = -8 and k = -40, so the vertex is (-8, -40) because vertex form is (h, k).

The axis of symmetry is x = -8, because the axis of symmetry is x = h.

Answer:

-4 and -8

Step-by-step explanation:

(x+4)(x+8) = 0

x+4 = 0 or x +8 = 0

x = -4 or x = -8

Answer:

greatest to least: cindy, betty, alice

Step-by-step explanation:

multiply each amount by 20- 5 days times 4 weeks

3*20=60 for alice

25*3=75 betty

75*3=225 cindy

Answer:

[tex](x - 3) \: (x - 8)[/tex]

Step-by-step explanation:

We were given the equation:

[tex] {x}^{2} - 11x + 24 = 0[/tex]

Therefore in order to factorize we first need to find the numbers that add to be equal to -11 and multiply to be equal to 24. The two numbers are:

[tex] - 8 \: and \: - 3 \\ \\ - 8 + ( - 3) = - 11 \\ - 8 \times - 3 = 24[/tex]

So the new equation is

[tex]{x}^{2} - 8x - 3x + 24 = 0 \\ \\ factorize: ( {x}^{2} - 8x) \: ( - 3x + 24) = 0 \\ \\ x(x - 8) \: - 3(x - 8) \\ \\ therefore : (x - 3) \: ( x - 8) = 0[/tex]

Answer:

Step-by-step explanation:

Comment

There are a lot of choices. Luckily the middle term is minus and the third term is plus, so you don't have to juggle minus signs around. Both factors are minus when put together with x.

-3 - 8

-4 - 6

-2 -12

-1 - 14

I think these are all the possible factors.

-4 + - 6 = - 10  Not the answer. It needs to be - 11

-2 + -12 = -14  Not the answer. It needs to be - 11

-1 + - 24 = -25 Just about as far away as you can get. Not the answer

So A must be right

-3 + -8 = - 11

That's what it should be. So the factors are

Answer:

(x -3)(x - 8)= x^2 - 11x + 24

Answer:

Step-by-step explanation:

Use the formula:

Plug In:

22,411 ÷ 2 - 260

Solve:

Answer is L = 10,945.5 inches
explain: perimeter is all 4 sides added together

We know one side is 260
we know the perimeter is 22,411

260 + 260 + L + L = 22,411
combine like terms

520 + 2L = 22,411
subtract 520 from both sides to isolate 2L

2L = 21,891
divide both sides by 2 to isolate L

L = 10,945.5 inches

Answer:

$70.76 or 70.7595

Step-by-step explanation:

Here’s the function:

67.39(1+0.05)^1

Hope this helps! ;-)

As per the given data, the vertices of the reflected parallelogram are C'(-4,8), D'(-2,4), E'(6,3), and F'(4,7).

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length and parallel to each other, and the opposite angles are also equal.

To reflect the parallelogram CDEF across the line y=2, we need to reflect each vertex across the line.

The line y=2 acts as a mirror, so the distance of each point to the line will remain the same before and after reflection, but the sign of the y-coordinate will change.

The reflection of point (x, y) across the line y=2 can be found by the formula (x, 2 - (y-2)) or (x, 4 - y).

Using this formula, we can find the coordinates of the reflected parallelogram:

- The reflected image of point C(-4,-4) is (-4, 8).

- The reflected image of point D(-2, 0) is (-2, 4).

- The reflected image of point E(6, 1) is (6, 3).

- The reflected image of point F(4, -3) is (4, 7).

Therefore, the vertices of the reflected parallelogram are C'(-4,8), D'(-2,4), E'(6,3), and F'(4,7).

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Alone, this shape cannot have the area solved in one step.  So, you must break it up into multiple pieces.

For this, we can break it up into a rectangle, and a right triangle.

The area formula for a rectangle is [tex]area = l*w[/tex]

The area formula for a right triangle is [tex]area = \frac{1}2} b*h[/tex]

To find the area of the rectangle, multiply 14 * 18 = 252 m^2

To find the length of the triangle, subtract 20 - 14 = 6

To find the height of the triangle, subtract 18 - 11 = 7

So, it is [tex]\frac{1}{2} 6*7[/tex] = 21 m^2

21 + 252 = 273 meters squared

Hope this helps, feel free to ask any questions

- Jeron    :)