Colin invests £2900 into his bank account,
He receives 3% per year compound interest.
How much will Colin have after 4 years?
Give your answer to the nearest penny where appropriate.

Answer:

As you can see, the -4 and -1/4 coefficient values are automatically different, and will resultantly produce different answers in the solutions.

The solutions are related, as the two numbers are reciprocals, as well as both being negative values.

Hope this helped !

Step-by-step explanation:

1)

a-13b

2) b

3) -3d+14e

4)12x-11y

5)-3rs

6)8xy-10cs

7)

[tex] - 2 {x}^{2} - 4x + 7[/tex]

8)

[tex]8 {y}^{2} - 7[/tex]

Answer:

1. 6a - 3b

2. b + 6c

3.- 3d - 2e

4. 12x + 5y

5. -3rs - 14bc

6. 8xy - 8cs

7. -2x^2 - 8x + 3

Step-by-step explanation:

Subtract polynomials

Answer:

answer is rounded to the nearest tenth D, 6.3

Step-by-step explanation:

just plug those numbers into the distance formula

Answer:

-8x-28 is after the distributive prop simplified

Step-by-step explanation:

4(-2x-7)

(4×-2x)-(4×-7)= -8x-28

Answer:

Step-by-step explanation:

B =20+20 = 40

Then because the side issue B and issue C are congruent their angles are congruent so angle C = 40

A triangle is 180 total so subtract B and C to find A

A = 180-40-40 = 100

I do not remember the names of all the theorems.

Answer:

आपको अपने पापों के लिए पश्चाताप करना चाहिए । वे तुम्हें नष्ट कर देंगे । आप कोई मौका नहीं खड़े हैं । तुम उसके हाथ पर मर जाओगे । पछताना

Step-by-step explanation:

its just so simple! :D

Answer:

Step-by-step explanation:

-8x³y²(x²-4y) = -8x³y²x² + 8x³y²4y

= -8x³⁺⁵y² + 32x³y²⁺¹

= -8x⁸y² + 32x³y³

Answer:

5, 6

Step-by-step explanation :

Answer:

25

Step-by-step explanation:

the angles and complementary so they add up to equal 90

90-65=25 so x = 25

Answer:

I really dont know

Step-by-stwp explanation:

98

Answer

The corresponding angles of the triangles are congruent

The image is a reduction of the pre-image

Neither the dilation nor the rotation change the shape of the triangle

Explanation:

For shapes to be similar:

1- there should be a ratio between the sides

2- angles in first shape should be congruent to angles in second shape

Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes

Let's check the choices:

1- The corresponding sides of the triangles are congruent:

This option is incorrect as dilation changes the lengths of the sides

2- The corresponding angles of the triangles are congruent:

This option is correct as neither dilation nor rotation alters the measures of the angles

3- The corresponding sides of the image are 5 times as long as those of the pre-image:

This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image

4- The image is a reduction of the pre-image:

This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced

5- Neither the dilation nor the rotation change the shape of the triangle:

This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths)

6- The rotation reduces the size of the triangle:

This option is incorrect as rotation does not alter the size of the shape. It only changes its position

Hope this helps :)

Options 2, 4 and 5 are the correct answer.

Given that, a triangle is dilated by a scale factor of 1/5 and then rotated 90 degrees clockwise about the origin.

A scale factor is defined as the ratio between the scale of a given original object and a new object, which is its representation but of a different size.

Now, a scale factor of 0.2 means that the sides of the image are 0.2 of the length of the original shape. However, angles are not changes

Let's check the choices:

1- The corresponding sides of the triangles are congruent:

This option is incorrect as dilation changes the lengths of the sides.

2- The corresponding angles of the triangles are congruent:

This option is correct as neither dilation nor rotation alters the measures of the angles.

3- The corresponding sides of the image are 5 times as long as those of the pre-image:

This option is incorrect as the sides of the image are only 0.2 times as long as those of the pre-image.

4- The image is a reduction of the pre-image:

This option is correct as the sides of the image are 0.2 times those of the pre-image which means that the shape is reduced.

5- Neither the dilation nor the rotation change the shape of the triangle:

This option is correct as both dilation and rotation are rigid transformations that do not alter the shape of the triangle (a triangle remains a triangle only with different side lengths).

6- The rotation reduces the size of the triangle:

This option is incorrect as rotation does not alter the size of the shape. It only changes its position.

Therefore, options 2, 4 and 5 are the correct answer.

To learn more about the scale factor visit:

https://brainly.com/question/22312172.

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Answer:

see below

Step-by-step explanation:

Answer in your own words:

Scale factor = Dimensions of the new shape ÷ Dimensions of the original shape. Which can also be used to calculate the dimensions of the new figure or the original figure by simply substituting the values in the same formula.  

• The scale factor of a dilated figure is denoted by 'r' or 'k'.

• If the scale factor is more than 1 (k > 1), the image is enlarged.

• If the scale factor is less than 1 (0< k <1), the image is contracted.

• If the scale factor is 1 (k = 1), the image remains the same.

• The scale factor cannot be zero.

Scale factor = k

Pre-image lengths: a, b  

(perimeter = 2a + 2b)

Image lengths: ka, kb

(perimeter = 2ka + 2 kb or k (2a + 2b))

Marissa needs to say that the perimeter of the image is the perimeter of the pre-image times the same scale factor.

area of the pre-image = ab

area of the image = (ka)(kb) or k^2 (ab) (The area of the image is the area of the preimage times the square of the scale factor)

Scale factor 5 (then repeat it with scale factor 6)

length of the pre-image = 3 x 4  

(perimeter = 2 (3 + 4) = 2(7) = 14)

length of the image = (3x5) x (4x5) = 15 x 20= 300

(perimeter = 2 (15 + 20) = 2 (35) = 70 or 14 x 5 = 70  

area of the pre-image = 3 x 4 = 12

area of the image = 15 x 20 = 300

12 x (5^2) = 12 x 25 = 300  

Answer: I believe the answer is 60

Step-by-step explanation:

9/12 = 3/4

If we do cross multiplying x over 80 times 3/4 it equals 60.

I am sorry if it is not correct I'm not fully sure but I hope this helped!!

Answer:

8

Step-by-step explanation:

2+6m+7=57

6m=57-7-2

6m=50-2

6m=48

m=48/6

m=8

Answer:

= 8

Step-by-step explanation:

Brainliest?

Answer:

Constants: 8 and 10

Step-by-step explanation:

Answer:

see below, I hope it's helpful

Step-by-step explanation:

Simplifying expressions...

1. use as many steps as you need, don't take shortcuts or try to do too much in one step... only touch each item in the expression once at most at each step

2. Follow PEMDAS

3. consider some of the rules of exponents: (a/b)^n = (a^n)/(b^n) and (x)^(-n) = 1/(x^n) and a^(b^c) = a^(bc)

examples x^(-4) = 1/(x^4)

                3^(-x) = 1/(3^x)

                (2/x)^(-n) = (1/(2/x))^n = (x/2)^n

                 2^(-x^3) = 2^(-3x) = 1/(2^3x)

so for example

2^(-x) - (x)^(-n) + (-n)^(x^(-2)) touch each part only once, do what you can

1/(2^x) - 1/(x^n) + (-n)^(-2x) the third part needed two steps, so be it

1/(x^n) - 1/(x^n) + (1/((-n)^2x)

Answer:

1. a) The scale factor that transform ΔKLP to ΔK'L'P' is a dilation of 3/2

b) The rule represented is that if the scale factor is larger than 1, the image formed is larger than the preimage

2. a) The scale factor of the dilation is 3/4

b) The rule represented by the dilation is a scale factor of less than 1 produces an image with a distance from a given point which is less than the distance of the preimage from the given point

Step-by-step explanation:

1. The coordinates of the triangle ΔKLP are;

K(-4, 2), L(2, 6), P(4, -6)

The coordinates of the points of triangle ΔK'L'P' are;

K'(-6, 3), L'(3, 9), P'(6, -9)

The length of segment KL = √((2 - (-4))² + (6 - 2)²) = 2·√13

The length of segment LP = √((4 - 2)² + (-6 - 6)²) = 2·√37

The length of segment KP = √((4 - (-4))² + (-6 - 2)²) = 8·√2

The length of segment K'L' = √((3 - (-6))² + (9 - 3)²) = 3·√13

The length of segment L'P' = √((6 - 3)² + (-9 - 9)²) = 3·√37

The length of segment K'P' = √((6 - (-6))² + (-9 - 3)²) = 12·√2

Therefore, K'L'/KL = 3·√13/(2·√13) = L'P'/LP = (3·√37/(2·√37)) = K'P'/KP =(12·√2/(8·√2)) =  3/2

Therefore, the scale factor that transform ΔKLP to ΔK'L'P' is a dilation of 3/2

The rule represented is that if the scale factor is larger than 1, the image formed (here ΔK'L'P') is larger than the preimage (ΔKLP)

2. The location of the preimage, W(-12, -4), the location of the image after the dilation W'(-9, -3)

Taking the origin O(0, 0), as the center of dilation, we have;

The length of the preimage W(-12, -4) from the origin = √((-12 - 0)² + (-4 - 0)²) = 4·√10

The length of the image W'(-9, -3) from the origin = √((-9 - 0)² + (-3 - 0)²) = 3·√10

Therefore, the scale factor of the dilation = W'O/WO = 3·√10/(4·√10) = 3/4

The scale factor of the dilation = 3/4

The rule represented by the dilation is that for a scale factor less than 1, the distance between the point of the image from a given point is less than the distance of the point of the preimage from the same point

Answer:

about 31 percent

Step-by-step explanation:

Since Joe has read 30% of the book, that means that 14 pages is 70% of the book. That means that two pages equals 10%. Therefore, the book has 20 pages.

70% = 14

so 30% = 6

total pages = 14+6=20

Answer:

14x² + 41x + 15

Step-by-step explanation:

............

Answer:

Step-by-step explanation:

negative b plus or minus the square root of b squared minus four times a times c all over 2a

Answer:

73:42

Step-by-step explanation:

1115-73=42

G : B

73 : 42

Answer:

the answer is f(n)=14.5−1.4n

Step-by-step explanation:

Hope this helps

The function models the n term of the given sequence is f(n)=14.5+1.4(n-1). Therefore, option B is the correct answer.

An arithmetic sequence is a sequence of numbers where the differences between every two consecutive terms is the same. The general form an arithmetic sequence is an=a+(n-1)d

The given arithmetic sequence is 14.5, 13.1, 11.7, 10.3,....

Here, a=14.5 and d=14.5-13.1=1.4

Substitute a=14.5 and d=1.4 in an=a+(n-1)d, we get

f(n)=14.5+1.4(n-1)

The function models the n term of the given sequence is f(n)=14.5+1.4(n-1). Therefore, option B is the correct answer.

To learn more about an arithmetic sequence visit:

https://brainly.com/question/10396151.

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Answer:

79456.1

Step-by-step explanation:

is it 794.561 × 10(2)?

Answer:

7

Step-by-step explanation:

a squared + b squared = c squared

plug it in to get

4 root 2 squared +b squared = 9 squared

(4 root 2)(4 root 2)=32

and 9 squared is 81

so the equation is

32+b squared = 81

subtract 32

b squared = 49

square root both sides

b=7

The length of the  missing side is [tex]3\sqrt{5}[/tex]

The square of the hypotenuse is equal to the sum of the square of the other two sides

From the given diagram;

Get the unknown side "x"

[tex]81 = 32 + x^2\\x^2 = 81 - 36\\x^2 = 45\\x = 3\sqrt{5}[/tex]

Hence the length of the  missing side is [tex]3\sqrt{5}[/tex]

Learn more on pythagoras theorem here: https://brainly.com/question/343682

Answer:

169.70

Step-by-step explanation:

Answer:

120[tex]\sqrt{2}[/tex]

Step-by-step explanation:

3[tex]\sqrt{40}[/tex] · 4[tex]\sqrt{5}[/tex] = (3[tex]\sqrt{5}[/tex]·[tex]\sqrt{4}[/tex]·[tex]\sqrt{2}[/tex]) x 4[tex]\sqrt{5}[/tex]

= 3 · 2 · 5 · 4 [tex]\sqrt{2}[/tex]

= 120[tex]\sqrt{2}[/tex]

Answer: Choice A.  (8, 4)

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

Explanation:

Because x = 2y, we can replace every copy of x with 2y

Let's do so in the second equation

3x - 4y = 8

3(x) - 4y = 8

3(2y) - 4y = 8 .... x replaced with 2y; now let's isolate y

6y - 4y = 8

2y = 8

y = 8/2 ..... divide both sides by 2

y = 4

Use this y value to find x

x = 2y

x = 2*4

x = 8

So we have x = 8 and y = 4 pair together to get the answer (x,y) = (8, 4) which is choice A.

Answer:

Commutative property of addition: Changing the order of addends does not change the sum.

Step-by-step explanation:

For example, 4 + 2 = 2 + 4 4 + 2 = 2 + 4 4+2=2+44, plus, 2, equals, 2, plus, 4.

Answer:

That means the missing side length is 15

Step-by-step explanation:

We use the Pythagorean theorem to find the hypotenuse. The hypotenuse for this triangle is 17. The equation for the Pythagorean theorem is a^2 + b^2 = c^2. Our equation is x^2+64 = 289. We can now subtract 64 from both sides and get 225. The square root of 225 will be 15.

Answer:

hi

Step-by-step explanation:

[tex] {c}^{2} = {a}^{2} + {b}^{2} \\ {8}^{2} + {b}^{2} = {17}^{2} \\ {b}^{2} = {17}^{2} - {8}^{2} \\ {b}^{2} = 289 - 64 \\ {b}^{2} = 225 \\ b = \sqrt{225} \\ b = 15[/tex]

hope it helps

Have a nice day

byee