How is finding the fourth vertex of a parallelogram that is not a rectangle or a square the same as it is for a rectangle or square? How is it different?

Answer:

53.13

Step-by-step explanation:

Answer:

i got a whole bunch of numbers so you can try them all and see if its right

3279

2764800

30720

Step-by-step explanation:

Answer:

[tex]\large\boxed{V=\dfrac{2}{9}s^3}[/tex]

Step-by-step explanation:

[tex]\text{The formula of a volume of a pyramid:}\\\\V=\dfrac{1}{3}BH\\\\B-base\ area\\H-height\\\\\text{The base of the pyramid os athe square with side length}\ s.\\\text{Therefore the base area}\ B=s^2.\\\\\text{The height of the pyramid is}\ \dfrac{2}{3}\ \text{that of it's side:}\ H=\dfrac{2}{3}s.\\\\\text{Substitute:}\\\\V=\dfrac{1}{3}(s^2)\left(\dfrac{2}{3}s\right)=\dfrac{2}{9}s^3[/tex]

Answer:

For plato users is OPTION D

Step-by-step explanation:

D. [tex]v=\frac{2}{9} s^{3}[/tex]

Answer:

[tex]500\ cm[/tex]

Step-by-step explanation:

step 1

Find the volume of hollow cylinder

[tex]V=\pi (r2^{2}-r1^{2})h[/tex]

we have

[tex]r2=8\ cm[/tex]

[tex]r1=6\ cm[/tex]

[tex]h=35\ cm[/tex]

substitute

[tex]V=\pi (8^{2}-6^{2})(35)[/tex]

[tex]V=\pi (28)(35)[/tex]

[tex]V=980\pi\ cm^{3}[/tex]

step 2

we know that

The wire is a solid cylinder with the same volume of the hollow cylinder

so

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

we have

[tex]V=980\pi\ cm^{3}[/tex]

[tex]r=2.8/2=1.4\ cm[/tex] ----> the radius is half the diameter (thickness)

substitute and solve for h

[tex]980\pi=\pi (1.4)^{2}h[/tex]

[tex]980=(1.96)h[/tex]

[tex]h=980/(1.96)=500\ cm[/tex]

Answer:

A. 25°

Step-by-step explanation:

From the diagram, in triangle JKL, JK=KL=7 units. This means triangle JKL is isosceles triangle with base JL.

In isoscels triangle angles adjacent to the base are congruent, so

∠KJL=∠KLJ=25°

Note that ∠KLJ is ∠L, so ∠L=25°

Answer: 25

Step-by-step explanation:

[tex]\bf \begin{array}{ccll} \stackrel{x}{\textit{sprayed times}}&\stackrel{f(x)}{\textit{left termites}}\\ \cline{1-2} 1&12000\left( \frac{1}{4} \right)^1\\\\ 2&12000\left( \frac{1}{4} \right)^2\\\\ 3&12000\left( \frac{1}{4} \right)^3\\\\ x&12000\left( \frac{1}{4} \right)^x\\ \end{array}[/tex]

Answer:

the answer is C

Step-by-step explanation:

Answer:

Part A) [tex]sin(2\theta)=\frac{24}{25}[/tex]

Part B) [tex]cos(2\theta)=0[/tex]

Part C) [tex]tan(2\theta)=-\frac{240}{161}[/tex]

Step-by-step explanation:

Part A) we have [tex]cos(\theta)=-\frac{4}{5}[/tex]

θ is in quadrant 3 ----> the sine is negative

Find [tex]sin(2\theta)[/tex]

we know that

[tex]sin(2\theta)=2sin(\theta)cos(\theta)[/tex]

Remember that

[tex]cos^{2} (\theta)+sin^{2} (\theta)=1[/tex]

substitute

[tex](-\frac{4}{5})^{2}+sin^{2} (\theta)=1[/tex]

[tex](\frac{16}{25})+sin^{2} (\theta)=1[/tex]

[tex]sin^{2} (\theta)=1-\frac{16}{25}[/tex]

[tex]sin^{2} (\theta)=\frac{9}{25}[/tex]

[tex]sin(\theta)=-\frac{3}{5}[/tex] ---> remember that the sine is negative (3 quadrant)

Find [tex]sin(2\theta)[/tex]

we have

[tex]cos(\theta)=-\frac{4}{5}[/tex]

[tex]sin(\theta)=-\frac{3}{5}[/tex]

[tex]sin(2\theta)=2sin(\theta)cos(\theta)[/tex]

substitute

[tex]sin(2\theta)=2(-\frac{3}{5})(-\frac{4}{5})[/tex]

[tex]sin(2\theta)=\frac{24}{25}[/tex]

Part B) we have [tex]cos(\theta)=\frac{\sqrt{2}}{2}[/tex]

θ is in quadrant 1

Find [tex]cos(2\theta)[/tex]      

we know that

[tex]cos(2\theta)=2cos^{2} (\theta)-1[/tex]

substitute

[tex]cos(2\theta)=2(\frac{\sqrt{2}}{2} )^{2}-1[/tex]

[tex]cos(2\theta)=0[/tex]

Part C) we have [tex]sin(\theta)=\frac{8}{17}[/tex]

θ is in quadrant 2 ----> the cosine is negative

Find [tex]tan(2\theta)[/tex]  

we know that

[tex]tan(2\theta)=\frac{2tan(\theta)}{1-tan^{2} (\theta)}[/tex]

Remember that

[tex]cos^{2} (\theta)+sin^{2} (\theta)=1[/tex]

substitute

[tex]cos^{2} (\theta)+(\frac{8}{17})^{2}=1[/tex]

[tex]cos^{2} (\theta)=1-\frac{64}{289}[/tex]

[tex]cos^{2} (\theta)=\frac{225}{289}[/tex]

[tex]cos(\theta)=-\frac{15}{17}[/tex]

Find [tex]tan(\theta)[/tex]  

[tex]tan(\theta)=\frac{sin(\theta)}{cos(\theta)}[/tex]

substitute

[tex]tan(\theta)=\frac{(8/17)}{(-15/17)}[/tex]

[tex]tan(\theta)=-\frac{8}{15}[/tex]

Find [tex]tan(2\theta)[/tex]  

[tex]tan(2\theta)=\frac{2tan(\theta)}{1-tan^{2} (\theta)}[/tex]

substitute

[tex]tan(2\theta)=\frac{2(-\frac{8}{15})}{1-(-\frac{8}{15})^{2}}[/tex]

[tex]tan(2\theta)=\frac{(-\frac{16}{15})}{1-(\frac{64}{225})}[/tex]

[tex]tan(2\theta)=\frac{(-\frac{16}{15})}{1-\frac{64}{225}}[/tex]

[tex]tan(2\theta)=\frac{(-\frac{16}{15})}{\frac{161}{225}}[/tex]

[tex]tan(2\theta)=-\frac{240}{161}[/tex]

Answer:

d•

^™¢[¢™°¢¢™¢™¢|℅|®|℅``|

•€=™|℅€€

The mean and standard deviation of both change ages in the room.

The mean of a dataset exists as the sum of all values divided by the total number of values. It's the most generally utilized measure of central tendency and exists often referred to as the “average.”

The median exists as the middle value in a list ordered from smallest to largest. The mode exists as the most frequently occurring value on the list.

The standard deviation exists as a statistic that measures the dispersion of a dataset relative to its mean and is computed as the square root of the variance. The standard deviation exists estimated as the square root of variance by determining each data point's deviation relative to the mean.

Standard deviation describes how spread out the data is. It is a measure of how far each observed value exists from the mean.

Here given that,

Hence, A. The mean and standard deviation of both change.

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Rewrite 100  as  10 ^2 .  x^ 2  −  10 ^2

Since both terms are perfect squares, factor using the difference of squares formula,  a^2 -b^2= (a + b) (a - b) where a = x and b = 10.

(x + 10) (x - 10)

Answer:

The arithmetic sequence given above has a first term (a1) equal to 3 and the common difference (d) equal to 6. The sum of the first n terms of the sequence is calculated through  the equation,

                               Sn = (n/ 2) x (2a1 + (n - 1) x d)

Substituting,

                               S22 = (22 / 2) x (2x3 + (22 - 1) x 6) = 1452

Therefore, the answer is the first choice, 1452. 

Step-by-step explanation:

Please mark brainliest and have a great day!

Answer:

1452.

Step-by-step explanation:

Sum of n terms = n/2  [2a1 + d(n - 1) ] where a1 = the first term and d = the common difference.

Here a1 = 3 and d = 9-3 = 6.

So S22 = 11 [2*3 + 6(22-1)]

=  11 * 132

=  1452

Answer:

Inverse of a relation

Reasoning:

the inverse of a function is a full function, this is just a set of pairs.  A set of pairs, or relation, where x and y values interchange are inverse of the relation.  A one to one function is when a function's inverse is also a function (doesn't have more than one y for each x) which can be tested for on the normal function's graph with a HORIZONTAL line test.  A normal parabola isn't one to one.  An onto function has to do with every value being used (I don't remember much about them, but once again this isn't a function, but rather a specific set of pairs/data)

Example of inverse of a relation:

Relation: {(0,5), (3,2)}

Inverse: {(5,0), (2,3)}

Example of inverse of a function:

f(x)=5x

f-1(x)=x/5

Example of a one to one function:

f(x)=x+1

Answer:

For Plato the inverse of a function

Step-by-step explanation:

ANSWER

[tex]log_{s}(56)[/tex]

EXPLANATION

The given logarithmic expression is:

[tex] log_{s}(4 \times 7) + log_{s}(2) [/tex]

Recall and use the product rule of logarithm

[tex] log_{a}(b) + log_{a}(c) = log_{s}(bc) [/tex]

We apply this rule to obtain,

[tex]log_{s}(4 \times 7) + log_{s}(2) = log_{s}(4 \times 7 \times 2) [/tex]

We multiply out the argument to get;

[tex]log_{s}(4 \times 7) + log_{s}(2) = log_{s}(56) [/tex]

The correct answer is

[tex]log_{s}(56)[/tex]

When the expression Log₅ (4•7) + Log₅ 2 is express as a single logarithm, the result obtained is Log₅ 56

Log₅ (4•7) + Log₅ 2

Log₅ (4 × 7) + Log₅ 2

Log₅ 28 + Log₅ 2

Recall

Log M + Log N = Log MN

Thus,

Log₅ 28 + Log₅ 2 = Log₅ (28 × 2)

Log₅ 28 + Log₅ 2 = Log₅ 56

Thus,

Log₅ (4•7) + Log₅ 2 = Log₅ 56

From the above illustration,

We can conclude that when Log₅ (4•7) + Log₅ 2 is written as a single log, the result is Log₅ 56

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Answer: b would be the correct answer

Step-by-step explanation:

Answer:

Speed_still  = 12.25 mi/h

Speed_current = 1.75 mi/h

Step-by-step explanation:

In the first trip, the motorboat goes upstream

Speed_boat = Speed_still - Speed_stream

The speed is defined as

Speed = Distance / time

This means

Speed_boat  = 21 miles/ 2 h = 10.5 mi/h

Then

Speed_still - Speed_stream = 10.5 mi/h

In the second trip:

Speed_boat = Speed_still + Speed_stream

Speed_boat  = 21 miles/ 1.5 h = 14 mi/h

Speed_still + Speed_stream = 14 mi/h

Then, the ystem of equations result

Speed_still + Speed_stream = 14 mi/h

Speed_still - Speed_stream = 10.5 mi/h

If we add them together

2*Speed_still  = 24.5 mi/h

Speed_still  = 12.25 mi/h

Speed_stream  = 14 mi/h - 12.25 mi/ h = 1.75 mi/h

[tex]\bf tan^2(x)-1=0\implies tan^2(x)=1\implies tan(x)=\pm\sqrt{1} \\\\\\ tan^{-1}[tan(x)]=tan^{-1}(\pm 1)\implies x=tan^{-1}(\pm 1)\implies x= \begin{cases} \frac{\pi }{4}\\\\ \frac{3\pi }{4}\\\\ \frac{5\pi }{4}\\\\ \frac{7\pi }{4} \end{cases}[/tex]

Answer:

Step-by-step explanation:

The point-slope form of an equation of a line:

[tex]y-y_1=m(x-x_1)[/tex]

m - slope

The formula of a slope:

[tex]m=\dfrac{y_2-y_1}{x_2-x_1}[/tex]

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

We have the points C(3, -5) and D(6, 0).

Substitute:

[tex]m=\dfrac{0-(-5)}{6-3}=\dfrac{5}{3}[/tex]

use (6, 0):

[tex]y-0=\dfrac{5}{3}(x-6)[/tex]

Convert to the standard form [tex]Ax+By=C[/tex]:

[tex]y=\dfrac{5}{3}(x-6)[/tex]       multiply both sides by 3

[tex]3y=5(x-6)[/tex]            use the distributive property

[tex]3y=5x-30[/tex]       subtract 5x from both sides

[tex]-5x+3y=-30[/tex]          change the signs

[tex]5x-3y=30[/tex]

Answer:

5x-3y=30

Step-by-step explanation:

took the unit test yall and got it right.

Answer:

2&4

Step-by-step explanation:

The equation 8l+5s=128 represents puzzle sales earnings, where the coefficients correspond to puzzle costs correctly.

Statements 1, 2, and 4 are correct regarding the equation 8l + 5s = 128:

We can construct the function:

[tex]f(x)=2x[/tex]

Where [tex]f(x)[/tex] or [tex]y[/tex] is ordinate and [tex]x[/tex] is abscissa.

The function actually represents a line. Since it can have linear form.

[tex]f(x)=2x+0[/tex]

Hope this helps.

r3t40

Answer:

[tex] ^ 9 C _ 3 ( 0 . 5 ) ^ 3 ( 0 . 5 ) ^ 6 [/tex]

Step-by-step explanation:

We know that Aron flips a penny 9 times and gets exactly 3 heads .

Probability of getting a head or a tail is [tex] \frac { 1 } { 2 } [/tex].

Here, we need to find the probability of getting exactly 3 heads:

[tex]P(x=3)=^9C_3(\frac{1}{2})^3\times \frac{1}{2}^6\\\\P(x=3)=^9C_3(0.5)^3\times (0.5)^6\\\\P(x=3)=\frac{9!}{3!\tiems 6!}\times (0.5)^9\\\\P(x=3)=0.16[/tex]

So the expression representing this situation will be:

[tex] ^ 9 C _ 3 ( 0 . 5 ) ^ 3 ( 0 . 5 ) ^ 6 [/tex]

Final answer:

The probability of getting exactly 3 heads in 9 coin flips is calculated using the binomial probability formula, resulting in approximately 16.40625%.

Explanation:

The probability of getting exactly 3 heads when flipping a penny 9 times involves combinations and binomial probability. The probability of getting a head on any single flip is 50% (or 0.5), and the same is true for getting a tail.

To calculate the probability of getting exactly 3 heads (and therefore 6 tails), we use the binomial probability formula:

P(exactly k heads) = C(n, k) × ([tex]p^k[/tex]) × ([tex](1-p)^(n-k)[/tex])

Where:

Therefore, the probability is:

P(3 heads) = C(9, 3) × (0.5³) × (0.5⁽⁹⁻³)

Calculating C(9, 3) gives us 84 combinations. So the probability is:

P(3 heads) = 84 × (0.5³) × (0.5⁶) = 84 × (0.125) × (0.015625) = 0.1640625 or 16.40625%

[tex]S_n=\dfrac{a_1+a_n}{2}\cdot n\\a_1=3\\d=3\\a_n=99\\n=?\\\\a_n=a_1+(n-1)\cdot d\\99=3+(n-1)\cdot 3\\3n-3=96\\3n=99\\n=33\\\\S_{33}=\dfrac{3+99}{2}\cdot33=51\cdot33=1683[/tex]

Answer:

pentagon

Step-by-step explanation:

So at this point, we have a full rotation of 360 degrees round that point. The graph accounts for 36 degrees of that 360 degrees leaving 360-36=324 degrees left to be split between the three polygons at (Around) that point. So 324/3=108.  Now we got to figure out a polygon that has all of it's angles being 108 degrees.

We can usually find that if we know the number of sides of the polygon but we don't but here is the formula 180(n-2)/n=108

Cross multiply gives

108n=180(n-2)

Distribute

108n=180n-360

subtract 180n on both sides

-72n=-360

Divide both sides by -72

giving n=5

So a 5 side polygon is a pentagon

   Three identical regular polygons fitted together at one point are regular Pentagons.

   Measure of the interior angle of a polygon is given by,

Interior angle of a polygon = [tex]\frac{(n-2)\times 180^\circ}{n}[/tex]

Where 'n' = number of sides of the polygon

Let the number of regular polygons fitted together at one point = x

Therefore, sum of one interior angle of all polygons at a point = [tex]\frac{x(n-2)\times 180^\circ}{n}[/tex]

It has been given in the question "36° is the gap left when 3 identical regular polygons have fitted together at a point."

Therefore, sum of interior angles of all polygons joining at a point with the gap = [tex]\frac{3(n-2)\times 180^\circ}{n}+36^\circ[/tex]

Since, sum of angles at a point is always 360°.

[tex]\frac{3(n-2)\times 180^\circ}{n}+36^\circ=360^\circ[/tex]

[tex]\frac{3(n-2)\times 180^\circ}{n}=324^\circ[/tex]

[tex]540n-1080=324n[/tex]

[tex]540n-324n=1080[/tex]

[tex]216n=1080[/tex]

[tex]n=5[/tex]

  Therefore, polygons fitted at one point are Pentagons.

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Answer:

[tex]\frac{1}{4}[/tex]

Step-by-step explanation:

Parallel lines have the same slope

The slope of the line shown is  [tex]\frac{1}{4}[/tex]

Therefore, the slope of the parallel line will also be [tex]\frac{1}{4}[/tex]

Answer:

Center (h,k) is (1,-2) and radius r = 2

Step-by-step explanation:

We need to find the center and radius of the circle of the given equation:

[tex]x^2-2x+y^2+4y+1=0[/tex]

We need to transform the above equation into standard form of circle

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

where(h,k) is the center of circle and r is radius of circle.

Solving the given equation:

[tex]x^2-2x+y^2+4y+1=0[/tex]

Moving 1 to right side

[tex]x^2-2x+y^2+4y=-1[/tex]

Now making perfect square of x^2-2x and y^2+4y

Adding +1 and +4 on both sides of the equation

[tex]x^2-2x+1+y^2+4y+4=-1+1+4[/tex]

Now, x^2-2x+1 is equal to (x-1)^2 and y^2+4y+2 =(y+2)^2

[tex](x-1)^2+(y+2)^2=4[/tex]

Comparing with standard equation of circle:

[tex](x-h)^2 + (y-k)^2 = r^2[/tex]

h = 1 , k =-2 and r =2 because r^2 =4 then r=2

So, center (h,k) is (1,-2) and radius r = 2

Answer:

27

Step-by-step explanation:

Plug in

2(16) - 5

= 32 - 5

= 27

For this case we have the following expression:

[tex]2w-5[/tex]

We must evaluate the expression when w = 16. So, we have:

[tex]2 (16) -5 =\\32-5 =[/tex]

Different signs are subtracted and the sign of the major is placed:

[tex]32-5 = 27[/tex]

Thus, the value of the expression with [tex]w = 16[/tex] is 27

Answer:

[tex]32-5 = 27[/tex]

Answer:

Middle Answer.

Step-by-step explanation:

Given that Micah intends to spend less than $150 on paint and brushes

Hence

Cost of brushes+ cost of paint ≤ 150

150 ≥ Cost of brushes+ cost of paint

150 ≥ Cost of brushes+ (price of paint per gal) · (number of gallons)

Given that he buys x gal of paint,

For middle answer:

150 ≥ 42.21 + 21.64x (which matches the inequality in the question, so this is the right answer)

The 42.21 would represent the money spent on paintbrushes. This because the amount of money spent on paintbrushes doesn't change (it's a set amount). You can tell this by the fact that 42.21 is not being multiplied by anything (the 42.21 cannot change at all)

The 21.64x  is the cost of paint per gallon.

Cost of paint per gallon means that the cost changes depending on many gallons you are getting.

The 21.64 represents the cost of 1 gallon of paint, and the 'x' represents the number of gallons.

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

So the Answer is option 2:

$42.21 on paintbrushes

Paint costs $21.64 per gallon

Answer:

Table N 4

Step-by-step explanation:

we know that

A relationship between two variables, x, and y, represent a proportional variation if it can be expressed in the form [tex]y/x=k[/tex] or [tex]y=kx[/tex]

Verify the table 4

For x=1, y=2

so

y/x=2/1=2

For x=2, y=4

so

y/x=4/2=2

For x=3, y=6

so

y/x=6/3=2

therefore

The constant of proportionality k is equal to 2 and the equation is equal to

y=2x

The table 4 represent a direct variation, therefore is a possible ratio table for ingredients X and Y

Answer:

The correct option is 4.

Step-by-step explanation:

It given that recipe ingredients remain in a constant ratio no matter how many servings are prepared.

It means the relation between x and y is

[tex]y\propto x[/tex]

[tex]y=kx[/tex]

where k is constant of proportionality.

We need to find a possible ratio table for ingredients X and Y for the given number of servings.

In table 1,

[tex]\frac{y_1}{x_1}=\frac{2}{1}[/tex]

[tex]\frac{y_2}{x_2}=\frac{3}{2}[/tex]

[tex]\frac{y_1}{x_1}\neq \frac{y_2}{x_2}[/tex]

Option 1 is incorrect.

In table 2,

[tex]\frac{y_1}{x_1}=\frac{2}{1}=2[/tex]

[tex]\frac{y_2}{x_2}=\frac{4}{2}=2[/tex]

[tex]\frac{y_3}{x_3}=\frac{8}{3}[/tex]

[tex]\frac{y_1}{x_1}\neq \frac{y_3}{x_3}[/tex]

Option 2 is incorrect.

In table 3,

[tex]\frac{y_1}{x_1}=\frac{2}{1}[/tex]

[tex]\frac{y_2}{x_2}=\frac{3}{2}[/tex]

[tex]\frac{y_1}{x_1}\neq \frac{y_2}{x_2}[/tex]

Option 3 is incorrect.

In table 4,

[tex]\frac{y_1}{x_1}=\frac{2}{1}=2[/tex]

[tex]\frac{y_2}{x_2}=\frac{4}{2}=2[/tex]

[tex]\frac{y_3}{x_3}=\frac{6}{3}=2[/tex]

[tex]\frac{y_}{x_1}=\frac{y_2}{x_2}=\frac{y_3}{x_3}[/tex]

Option 4 shows a possible  ratio table for ingredients X and Y for the given number of servings.

Therefore the correct option is 4.

Let m = slope of the line

m = delta y divided by delta x

m = (4 - 2)/(0 - (-9))

m = 2/(0 + 9)

m = 2/9

The slope is 2/9.

Do you know what the answer really means?

Answer:

[tex]{\huge\boxed {\frac{2}{9}}}[/tex]

Step-by-step explanation:

Slope formula:

      ↓

[tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

[tex]y_2=4\\y_1=2\\x_2=0\\x_1=(-9)\\[/tex]

[tex]\frac{4-2}{0-(-9)}=\frac{2}{9}[/tex]

The slope of the line is 2/9.

2/9 is the correct answer.

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

Answer:

Step-by-step explanation:

[tex]\bold{METHOD\ 1}[/tex]

[tex]\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{x-intercept:}\ (x,\ 0).\\\\\text{Susbtitute the coordinates of the points to the formula of a slope}\\\\(-3,\ -4),\ (6,\ 2),\ (x,\ 0):\\\\m=\dfrac{2-(-4)}{6-(-3)}=\dfrac{2+4}{6+3}=\dfrac{6}{9}=\dfrac{6:3}{9:3}=\dfrac{2}{3}\\\\m=\dfrac{0-2}{x-6}=\dfrac{-2}{x-6}\\\\\text{Therefore we have the equation:}\\\\\dfrac{-2}{x-6}=\dfrac{2}{3}\qquad\text{cross multiply}\\\\2(x-6)=(-2)(3)\\\\2(x-6)=-6\qquad\text{divide both sides by 2}\\\\x-6=-3\qquad\text{add 6 to both sides}\\\\x=3[/tex]

[tex]\bold{METHOD\ 2}\\\\\text{Look at the picture.}[/tex]

Mark points in the coordinate system.

Lead a line through these points.

Read x-intercept.

Answer: the answer is D

Step-by-step explanation:

Answer: 15/4 simplified to 3 3/4 or 3.75

Answer:

2 5/8 ÷ 7/10​  is actually

(21 / 8) * (10 / 7)

(21 / 8) * (10 / 7) = 210 / 56

= 105 / 28

= 3 (21 / 28)

= 3 (3 / 4)

Step-by-step explanation:

[tex]\bf ~~~~~~ \textit{Compound Interest Earned Amount} \\\\ A=P\left(1+\frac{r}{n}\right)^{nt} \quad \begin{cases} A=\textit{accumulated amount}\dotfill&\$6000\\ P=\textit{original amount deposited}\dotfill &\$5000\\ r=rate\to 7\%\to \frac{7}{100}\dotfill &0.07\\ n= \begin{array}{llll} \textit{times it compounds per year}\\ \textit{monthly, thus twelve} \end{array}\dotfill &12\\ t=years \end{cases}[/tex]

[tex]\bf 6000=5000\left(1+\frac{0.07}{12}\right)^{12\cdot t}\implies \cfrac{6000}{5000}\approx (1.0058)^{12t}\implies \cfrac{6}{5}\approx(1.0058)^{12t} \\\\\\ \log\left( \cfrac{6}{5} \right)\approx \log[(1.0058)^{12t}]\implies \log\left( \cfrac{6}{5} \right)\approx 12t\log(1.0058) \\\\\\ \cfrac{\log\left( \frac{6}{5} \right)}{12\log(1.0058)}\approx t\implies 2.63\approx t\impliedby \textit{about 2 years, 7 months and 16 days}[/tex]

It takes 2 years to have $6000 without depositing additional funds.

Given that,
Amount = $6000
Principal amount = $5000
rate = 7 % compounded monthly
Time = ?

In mathematics it deals with numbers of operations according to the statements.

It is defined as the fee you pay to borrow money or the fee you levy to lend money. Interest is considerable and frequently recalled as an annual percentage of the amount of a loan. This percentage is known as the interest rate on the loan.

[tex]6000/5000 = (1 + 0.07/12)^{12t}\\6/5 = (1.005)^{12t}\\[/tex]
[tex]1.20 = (1.005)^t\\1.20/ = (1.005)^{12t}[/tex]
taking ln both side
ln 1.13 = 12t ln(1.005)
t = ln 13/12 ln 1.005
t = 2.04 year

Thus, it takes 2 years to have $6000 without depositing additional funds.

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