consider an investment of $6000 that earns 4.5% interest.


How long would it take for the investment
to reach $15,000 if the interest is
compounded monthly? Round your
answer to the nearest tenth.

Answer:

 its a geometric sequence where each term is 3 times the previous term.

Step-by-step explanation:

{2,6,18,54,162,486,1458...}

Step-by-step explanation:

yes right angle measure 90 degrees

mark me brainliest

Answer:

21/4

Step-by-step explanation:

Answer:

[tex]\frac{42}{8}[/tex]

Step-by-step explanation:

• First multiply the numerators:

6 x 7 = 42

• Then multiply the denominators:

(6 doesn't have a denominator, which is the same as having a denominator of 1)

1 x 8 = 8

∴ The answer is [tex]\frac{42}{8}[/tex] .

The equation of this circle in standard form is (x-2)² + (y+3)² = 18

The center of the circle is at the point  (2,-3), and its radius is 4.2426 units

Circle is the 2D geometry which is round in shape with radius R.

Given is the general form of the equation of a circle is

7x² + 7y² − 28x + 42y − 35 = 0.

Dividing by 7, we get

x² -4x + y² + 6x = 5

Completing the squares, we have

x² -4x + 4 + y² +6x + 9 = 5 +4 + 9

(x-2)² + (y+3)² = 18 = (3 √2)²

Circle's center is (2,-3) and  radius = 3 √2 = 4.2426 units

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Answer:

(x-2)^2 + (y+3)^2 = 18,

2,-3

3(2^(1/2)) units

Step-by-step explanation:

Below

Answer: 28,278.10

Step-by-step explanation:

[tex]a_{7} =16500(1.08)^7[/tex]

[tex]a_{7} =28278.1[/tex]

Answer:

the area of rectangle is 270 cm and its length is 18 cm

the breath of the perimeter of given rectangle respectively

used concept

area of rectangle l into b where is is v is breadth of the rectangle perimeter of rectangle 2 into l + b where I and b stands for same as the

solution

let's the length of rectangle is equal to l is equal to 18 cm

breath of rectangle is is equal to b is equal to

area of rectangle is equal to 270 CM

now according to the question and l into b is equal to a

18 into b is equal to 1070

b is equal to 270 upon 18

b is equal to 15 CM

p no no perimeter of the rectangle is equal to 2 into l + b

2 multiply 18 + 15

2 X 33

is equal to 66 cm

therefore the breath and the perimeter of rectangle are 15 cm and 66 respectively

The equation is 1.56 + 20x = 33.96 and the value of x is 1.62.

An equation is a mathematical statement with an 'equal to' symbol between two expressions that have equal values.

Here, Based on the given conditions, formulate: 1.56 + 20 × x = 33.96

Rearrange unknown terms to the left side of the equation:  20x = 33.96-1.56

Calculate the sum or difference: 20x = 32.4

Divide both sides of the equation by the coefficient of variable: x = 32.4/20

Calculate the product or quotient: x = 1.62

get the result: x = 1.62

Thus, the equation is 1.56 + 20x = 33.96 and the value of x is 1.62.

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Answer:

D

Step-by-step explanation:

The product of the slopes of two perpendicular lines is -1.

If the slopes of the diagonals are 1 and -1, then their product is -1, and they are perpendicular.

Answer: D

A sentence that describes what Talia should do to show that the diagonals of the square are perpendicular is: D. show that the slope of SQ is 1 and the slope of PR is -1.

In order for a quadrilateral to be a square, the two (2) pairs of its sides must be equal (congruent) and perpendicular to each other.

Therefore, we would have to calculate the slope of each side by using this mathematical equation:

Slope (m) = (y₂ - y₁)/(x₂ - x₁)

Slope (m₁) of SQ = (a - 0)/(a - 0)

Slope (m₁) of SQ = a/a = 1.

Slope (m₂) of PR = (a - 0)/(0 - a)

Slope (m₂) of PR = -a/a = -1.

Based on the condition for two (2) perpendicular lines, we have:

m₁ × m₂ = -1

1 × -1 = -1

-1 = -1

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Answer:

Step-by-step explanation:

Ok so you are given the values of the slope-intercept form with m being the slope and b being the y-intercept. So since b is equal to -1 you want to plot a point at (0, -1) since that is the y-intercept (when x = 0). The next thing you want to do is look at the slope, which is essentially saying each time x increases by 5 the y-value decreases by 4 or in other words rise/run which is negative which is why you're going down. So from the point (0, -1) go forward 5 units and go down 4 units which should lead you to (5, -5) and the third point you can plot is by going backwards instead of forwards. So instead of every time x increases by 5 y decreases by 4 you're going to do the inverse. Every time x decreases by 5, y is going to increase by 4. So by doing this from the y-intercept (0, -1) you should go backwards 5 units and up 4 units which should lead you to (-5, 3). And then now just draw a line that goes through all those three points. Hope that helps :)

Step-by-step explanation:

Hi There! Let me help you :)

[tex] = 8.8.8.8.8.8.8[/tex]

[tex] = ( \text{there \: are \: 7 \:numbers \: eight })[/tex]

[tex] \: [/tex]

So we can rewrite the above equation to be like this.

[tex] = 8.8.8.8.8.8.8[/tex]

[tex] = 8.(1 + 1 + 1 + 1 + 1 + 1 +1)[/tex]

[tex] = 8.7[/tex]

To me, Benjamin should use graph A to show the decrease in temperature. It would be best for Benjamin to use this graph for his presentation because the temperature decrease in this graph

The graphs that complete the question are added as an attachment

From the attached graph, we have the following highlights:

The above means that graph B is a misleading graph

Hence, Benjamin should use graph A for his report

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Answer:

swap x and y

Step-by-step explanation:

You can find an inverse function by replacing "x" and "y"

for example:

y = mx + b

becomes

x = my + b

if your equation is:

f(x) = 3(x²) - 3

{remember, f(x) means the same thing as y}

y = 3(x²) - 3

inverse:

x = 3(y²) - 3

this is it, hope this is helpful!!

Answer:

make every (x) a (y)

Answer: 38°

Using cosine rule,

a² = b² + c² -2bc cos(A)

Insert values from diagram

14² = 18² + 22.8² - 2(18)(22.8) cos(A)

196 = 324 + 519.84 - 820.8 cos(A)

-820.8 cos(A) = 196 - 324 - 519.84

-820.8 cos(A) = -647.84

cos(A) = -647.84/-820.8

A = cos^{-1} (-647.84/-820.8)

A = 37.88°

A ≈ 38°

Answer:

[tex]\boxed {38^{o}}[/tex]

Step-by-step explanation:

Applying Law of Cosines :

⇒ a² = b² + c² - 2bc(cos A)

⇒ 14² = 22.8² + 18² - 2(22.8)(18)(cos A)

⇒ 820.8(cos A) = 519.84 + 324 - 196

⇒ 820.8(cos A) = 647.84

⇒ cos A = 647.84/820.8

⇒ cos A = 0.789278752

⇒ m ∠A = cos⁻¹ (0.789278752)

⇒ m ∠A = 37.88 ≈ 38°

The value of n is 12. and m is 6root5

We have given the diagram,

The measurement of m,

n = 12

According to the altitude theorem

The right triangle altitude theorem or geometric mean theorem is a result in elementary geometry that describes a relation between the altitude on the hypotenuse in a right triangle and the two-line segments it creates on the hypotenuse.

24/n = n/6

The Cross multiply

24 * 6 = n²

144 = n²

n² = 144

n = √144

n = 12

[tex]m^2=6^2+n^2[/tex]

[tex]m^2=6^2+12^2\\m^2=36+144\\m^2=180[/tex]

[tex]m=\sqrt{180} \\m=2\cdot \:3\sqrt{5}\\m=6\sqrt{5}[/tex]

Hence the value of n is 12.

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Answer:

12

Step-by-step explanation:

Answer:

The first one (x=1 and y=1/2)

Step-by-step explanation:

The first table is the only one that has a constant rate of change.  The x value increases by 1, and the y value increase by 1/2.

Hope this helped :)

Answer:

The first one where x increases by 1 and y increases by 1/2.

Step-by-step explanation:

To find the equation, 1/2=1+b

Solve for b

1/2-1=-0.5

B=-0.5

Now, solve for x

1/2=x-0.5

As you can already see in the table, x increase by 1, so no need to even solve.

The equation would be y=1x-0.5 (I’ll post the graph in the picture to prove it is linear.

A linear equation is an equation of a straight line, which means that the degree of a linear equation must be 0 or 1 for each of its variables. In this case, the degree of variable yy is 1 and the degree of variable x is 1.

Answer:

2000 tickets were sold

Step-by-step explanation:

40% can also be written as 0.40

800/ 0.40 = 2000 total tickets

Answer:

lklklkj

Step-by-step explanation:

67890-

Answer:

y = -3x + 1

Step-by-step explanation:

The line crosses the y-axis at 1. This is called the y-intercept. This is the number you fill in for c in the form of the equation given.

You can pick any two points on the line to calculate the slope. But you can actually SEE the slope without having to calculate it when you have the graph to look at. See the line crossing the y-axis at 1. Look for another point (that has nice whole number coordinates) there is one DOWN3 and OVER1. If you notice, the next point is also DOWN3 and OVER1.

DOWN3 and OVER1 is the slope -3/1, which is equal to -3.

Fill in -3 in place of the m in the equation.

y = -3x + 1

Done!

Answer:

y = -3x + 1

Step-by-step explanation:

The equation of a line in slope/intercept form is y = mx + c where m is the slope and c the y-intercept(ie the value of y when x =0)

The slope can be found by taking any two points on the line,  (x1, y1) and (x2,y2) and computing (y2-y1)/(x2-x1)

If you look at the line 2 points on the line are P(2,-5) and (0,1)

Slope = (-5-1)/(2-0) = -3

The y-intercept is the y-value at which the line intersects the y-axis ie at x = 0 and you can see that this is 1

Therefore equation is
y = -3x + 1

You can check to see if this is correct by plugging in some other value of x and seeing if the correct y value corresponds to the equation y-value

For example, in the graph we see that at x = 1, y = -2

Indeed -3(1) + 1 = -3 + 1 = -2 also

Answer:

a

2

−

b

2

Since both terms are perfect squares, factor using the difference of squares formula,

a

2

−

b

2

=

(

a

+

b

)

(

a

−

b

)

where

a

=

a

and

b

=

b

.

Answer:

The vertex is the point of coordinates (-2 , 5)

Step-by-step explanation:

we notice that the equation of the parabola is given in vertex form :

y = -4(x + 2)² + 5

then

y = -4(x − (-2))² + 5

Therefore

The vertex of the graph is the point (-2 , 5)

Answer:

15 ($20 dollar bills) and 19 ($10 dollar bills) ! Pretty sure this is correct, if wrong let me know and i'll make a question for you to give your points back, i dont know if i can do that but i can try!! Have a good day.

Answer:

-1

Step-by-step explanation:

the answer snis negative One

[tex]\dfrac{6\sqrt 3~ \text{cis} \left( \dfrac{7 \pi} 6 \right)}{3 \sqrt 5 ~\text{cis} \left( \dfrac{\pi}{3}\right)}\\\\\\=\dfrac{2\sqrt 3 \cdot e^{i\tfrac{7\pi}{6}}}{\sqrt 5\cdot e^{i \tfrac{\pi}{3}}}\\\\\\=\dfrac{2 \sqrt 3}{\sqrt 5} \cdot \left(e^i \right)^{\tfrac{7\pi}{6} - \tfrac{\pi }{3}}~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~;\left[\text{cis}~ \theta = e^{i \theta}\right]\\\\\\=\dfrac{2 \sqrt{3}}{\sqrt 5} \cdot \left(e^i\right)^{\tfrac{5\pi}6}\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\cdot e^{i\tfrac{5 \pi}6}\\\\\\[/tex]

[tex]=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ \cos \left(\dfrac{5\pi}{6}\right) + i \sin \left(\dfrac{5\pi}{6}\right) \right]~~~~~~~~~~~~~~~~~~;\left[e^{i\theta} = \cos \theta + i \sin \theta} \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5}\left[ \cos \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) + i\sin \left(2 \times \dfrac{\pi}2 -\dfrac{\pi}{6} \right) \right]\\\\\\=\dfrac{2\sqrt{3}}{\sqrt 5} \left[ -\cos \left(\dfrac{\pi}{6}\right) + i \sin \left(\dfrac{\pi}{6}\right) \right]\\\\\\[/tex]

[tex]=\dfrac{2\sqrt{3}}{\sqrt 5}\left( -\dfrac {\sqrt{3}}{2} + i \cdot \dfrac 12 \right)\\\\\\=-\dfrac{3}{\sqrt 5} + i \dfrac{\sqrt 3}{\sqrt 5}[/tex]

Answer:

Step-by-step explanation:

Just took the test:

6sqrt3 cis (7pie/6)/ 3sqrt5 cis (pie/3)=

2sqrt15/5 cis (5pie/6)

Step-by-step explanation:

the picture and its text explain it actually already.

each block (or square) on each side represents a fraction.

the whole block is 1. the colored parts are the fraction of that whole (1).

we see the example 2/3 × 3/4

the left block with 2 out of 3 strips marked in pink shows us 2/3 (2/3 of the block is pink).

the right block with 3 out of 4 strips marked in purple shows us 3/4 (3/4 of the block is purple).

it is essential for this method to orient the strips in one block to be at a right angle with the strips of the other block.

now, to do the multiplication you overlay the strips of both blocks.

you see this creates a chess board pattern. the total number of little squares or rectangles is the denominator (bottom part) of the result. in this case 12.

the number of little squares or rectangles that are in both original strips is the numerator (the top part) of the result. in this case 6.

so, yes, 2/3 × 3/4 = 6/12, which can then be refined to 1/2.

now, you have to do the same thing with the actual examples (I cannot draw here, sorry) :

1/4 × 3/5 = 3/20

the left block with 4 strips (one in pink, or whatever color you want), the right block with 5 strips (and 3 marked in e.g. purple).

and then the result block with 4 columns and 5 rows creating 20 little squares or rectangles, and 3 of them are in all original strips.

and the same

3/5 × 2/3 = 6/15 = 2/5

1/2 × 2/5 = 2/10 = 1/5

Answer:

Her sales after 6 months are = 127units

Step-by-step explanation:

Percentage increase:- The degree to which a value increases expressed in percent form is known as percentage increase.

formula for % increase = (final value - initial value)/initial value(100)

Here in the question,

percentage increase after every month is = 5%

initial value  =  95 units

therefore by applying above formula :-

[(x-95)/95]×100 = 5          [where x is the value of her sales goals after 1 month]

x = (5/100)×95+ 95

x = 99.75

Now this x will be the initial value for the next month

x₂ = (5/100)99.75+ 99.75             [ x₂ = sales goal after 2 months]

x₂ = (5/100)×99.75+ 99.75

x₂ = 104.73

similarly,

(x₃-104.73/104.73)100 = 5       [x₃ = sales after 3 months]

x₃ = 109.96

similarly for 4th month,

(x₄ -109.96/109.96)100 = 5       [x₄ = sales after 4 months]

x₄ = 115.45

for 5th month,

(x₅ -115.45/115.45)100 = 5       [x₅ = sales after 5 months]

x₅ = 121.22

finally for the 6th month

(x₆-121.22/121.22)100 = 5        [x₆ = sales after 6 months]

x₆ = 127.28

therefore,

her sales after 6 months are = 127.28 units or 127 units by rounding off

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Triangles are similar and only differ in size meaning they are dilated

So first we have to find the scale factor of dilation (by how much the smaller triangle got bigger)

Find scale factor:

2.4a=4.8

z=2

Find x:

we multiply the original side of the small side with the scale factor of 2

2.8(2)=x

5.6=x

So, x=5.6

Answer:

75 km

Step-by-step explanation:

(50km/h)(1.5h) = 75km

Answer:

the answer is 6

Step-by-step explanation:

1. 3x+4=22

2. subtract 4 from both sides

3x+4=22

     -4=22

           -4

3. rewrite the equation   3x=18

4. divide 3 from both sides

3x/3=18/3

hint: 3x/3 cancels out so you just have x

5. divide 18 by 3

6.x=6

The answer is 4p² + 6p - 8 which is subtraction of one equation from the other in vertical format.

Polynomial is the combination of variables and constants systematically with "n" number of power in ascending or descending order.

[tex]\rm a_1x+a_2x^2+a_3x^3+a_4x^4..........a_nx^n[/tex]

We have two polynomial:

2p² + 3p - 4 and  -2p² - 3p + 4

Subtraction in a vertical format:

       2p² + 3p - 4

-      -2p² - 3p + 4

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

Changin sign of the expression -2p² - 3p + 4:

       2p² + 3p - 4

+      2p² + 3p - 4

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

Now adding like terms.

       2p² + 3p - 4

+      2p² + 3p - 4

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

       4p² + 6p - 8

Thus, the answer is 4p² + 6p - 8 which is the subtraction of one equation from the other in vertical format.

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Answer:

-12 ≤ p ≤ 12

Step-by-step explanation:

If the absolute value inequality is

|p| ≤ 12,

then the answer is

-12 ≤ p ≤ 12