the hypothenus of a right angle triangle is 13cm. if one other side of the triangle is 1cm shorter than the hypothenus, calculate the third side of the triangle
​

Answer:

315 cm²

Step-by-step explanation:

Given the scale factor of 2 similar figures is a : b , then

ratio of areas = a² : b²

Here the scale factor = 7 : 21 = 1 : 3 , thus

ratio of areas = 1² : 3² = 1 : 9

That is the area of the enlargement is 9 times the original, so

area of enlargement = 35 × 9 = 315 cm²

Answer:

increase by a factor of 3

Step-by-step explanation:

First you have to find the width,

35/7=5cm

Since the length had been increased to 21cm, we need to find the larger area,

21*5=105cm^2

now we just need to find how much has the area increased compare to the original area,

105/35=3

Answer:

C.

Step-by-step explanation:

6x-12y=18

6x=18+12y

Divide through by 6

X=3+2y

X=2y+3

Answer:

C

Step-by-step explanation:

6x-12y=18 x=2y+3 this is correct

Step-by-step explanation:

In my opinion Option A is the correct answer because

Product of 3 and x = 3x

7.5 more than that = 3x + 7.5

Answer:

the answer is option A

Step-by-step explanation:

product of 3 and x = 3x

7.5 more than the product of 3 and x = 3x+7.5

Answer:

f ≥ -2

Step-by-step explanation:

See steps below:

Answer:

f [tex]\geq[/tex] -2

Step-by-step explanation:

5f + 3 (−8f − 9) ≤ −8f −1 −4

=5f -24f -27 ≤ -8f -1 -4

= -19f -27 ≤ -8f -5

=-11f ≤ 22

= f [tex]\geq[/tex] -2

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

Work Shown:

Given info

P(A) = 7/20

P(A∩B)=49/400

P(B) = unknown

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

P(A∩B) = P(A)*P(B), assuming A and B are independent events

49/400 = (7/20)*P(B)

(7/20)*P(B) = 49/400

P(B) = (20/7)(49/400)

P(B) = (20*49)/(7*400)

P(B) = (20*7*7)/(7*20*20)

P(B) = 7/20

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

Note how

P(A∩B) = P(A)*P(B)

P(A∩B) = (7/20)*(7/20)

P(A∩B) = (7*7)/(20*20)

P(A∩B) = 49/400

which helps to confirm the answer.

Answer:

2. 3^2

Step-by-step explanation:

Use PEMDAS. First parenthesis, exponents (3^2), multiplication, division, addition, and subtraction.

The answer is 2 because you do the exponents in the parenthesis first.

Answer:

Perimeter of square = 24 meter

Step-by-step explanation:

Given:

Square divided into three equal rectangle

Perimeter of rectangle = 16 meter

Find:

Perimeter of square

Computation:

We know that rectangle are equal

So,

3b = l

Perimeter of rectangle = 2 (l + b)

16 = 2 (l + b)

16 = 2 (3b + b)

b = 2 meter

l = 3 (2) = 6 meter

Side of square = 6 meter

Perimeter of square = 4(side)

Perimeter of square = 4(6)

Perimeter of square = 24 meter

Answer:

7) 9.135x10^10

8) 3.428x10^-2

9) 2.5x10^-7

10) 4x10^10

Step-by-step explanation:

You’re only supposed to have one number to the left of the decimal point in scientific notation.

7) 9.135x10^10

8) 3.428x10^-2

9) 2.5x10^-7

10) 4x10^10

Answer:

1. 8+9÷3x(6-5)=11

2. 5+3-(8÷4)=4

Step-by-step explanation:

Answer:

1/4

Step-by-step explanation:

Find the area of the full rectangle:

=> 40 x 30 = 1200

Find the area of the uncut part:

=> 20 x 15

=> 300

Make these numbers as a fraction.

=> 300 / 1200

=> 3/12

=> 1/4

So, 1/4 part remains uncut.

The fractional part of the lawn remains uncut is 1/4

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

Given that A boy is mowing a rectangular lawn 40ft long and 30ft wide. He has cut all of it except for a rectangle that is 20ft long and 15ft wide.

To Find the area of the full rectangle:

40 x 30 = 1200

To Find the area of the uncut part:

= 20 x 15

= 300

Now Make these numbers as a fraction;

=> 300 / 1200

=> 3/12

=> 1/4

Therefore, 1/4 part remains uncut.

Hence, The fractional part of the lawn remains uncut is 1/4.

Learn more about the area;

https://brainly.com/question/1658516

#SPJ2

Answer: the probability would be 1:5

Step-by-step explanation: since there are 2 m you would put that on top and divide it by all the others and there are 10 of them and then simplifie it and get the answer

Answer:

P ( not M)= 4/5

Step-by-step explanation:

We want to find the probability that if a card is chosen, it does not have the letter M on it.

The probability can be found by creating a fraction with the number of cards that do not have M over the total number of cards.

P (not M) = cards without M / total cards

The word complement has 10 letters, therefore there is a total of 10 cards.

P (not M) = cards without M/ 10

There are 2 cards with an M. That will leave 8 cards without an M. (10 total cards - 2 cards with M= 8 cards without M).

P (not M)= 8/10

This fraction can be simplified. Both the numerator (top number) and denominator (bottom number) can be divided by 2.

P (not M)= (8/2) / (10/2)

P (not M)= 4/ (10/2)

P (not M) = 4/5

The probability of choosing a card without the letter M on it is 4/5

Answer:

. D. Yes, the more information provided by a researcher the better. Respondents can now give an informed opinion and the results will be more accurate.

Step-by-step explanation:

But again this could be an opinion answer as well

Hope this helps

If this seems incorrect anyway please just comment and I shall change my answer thanks very much :)

Answer:

27

Step-by-step explanation      divided 10 and 270

Answer:

15 Respondents

Step-by-step explanation:

Total number of respondents = n (PUBG ∪ M ∪ C) = 50

PUBG = n(PUBG ) = 15 people

Mobile legends = n(M) = 30 people

Clash of clans = n(C) = 20 people

n ( PUBG ∩ M) = Unknown

Step 1

The first step is to find the number of respondents that chose two or the games

a) Number of respondents that chose Mobile legends and PUBG =

n ( M ∩ PUBG)

30 - x = 15 - x + x

30 - 15 = x + x - x

15 = x

b) a) Number of respondents that chose Mobile legends and Clash of clans =

n ( M ∩ C)

n ( M ∩ C) = y

30 - y = 20 - y + y

30 - 20 = y + y - y

10 = y

c) Number of respondents that chose PUBG and Clash of clans =

n ( C ∩ PUBG) = z

20 - z = 15 - z + z

20 - 15 = z + z - z

5 = z

Step 2

How many Respondents chose all 3 online games

= n ( PUBG ∩ M)

n (PUBG ∪ M ∪ C) = n(PUB ) + n ( M ) + n (C) – n ( M ∩ PUBG) – n ( C ∩ PUBG) – n ( M ∩ C) + n (PUBG ∩ M ∩ C)

50 = 30 + 20 + 15 - 15 - 5 - 10 + n (PUBG ∩ M ∩ C)

50 = 65 - 30 + n (PUBG ∩ M ∩ C)

50 = 35 + n (PUBG ∩ M ∩ C)

50 - 35 = n (PUBG ∩ M ∩ C)

n (PUBG ∩ M ∩ C) = 15

Therefore, the number of Respondents chose all 3 online games = 15

Answer:

15

Step-by-step explanation:

Answer:

7x+2y<2 will have a shaded area below the boundary line

Answer:

1.1 cm or 7.9 cm

Step-by-step explanation:

Given:

Point D mark for 4.5 cm

Distance between points D and E =3.4 cm

Find:

Location of point E

Computation:

Assume;

Point o = 0 cm mark

Point E = Point D mark - Distance between points D and E

Point E = 4.5 cm - 3.4 cm

Point E = 1.1 cm

or

Point E = Point D mark + Distance between points D and E

Point E = 4.5 cm  + 3.4 cm

Point E = 7.9 cm

Answer:

Step-by-step explanation:

(3, -7)  ⇒   x = 3,   y = -7

x + y = 3 + (-7) = -4

3x + 2y = 3•3 + 2(-7) = 9 - 14 = -5

    x + y < -4                            3x + 2y < -5

A.

  -4 < - 4   ←  false                 -5  < -5   ← false

B.

  -4 ≤ - 4   ←  true                   -5  < -5   ←  false

C.

  -4 < - 4   ←  false                  -5  ≤ -5   ←  true

D.

   -4 ≤ - 4   ← true                  -5  ≤ -5   ← true

Answer:

D.  

x + y ≤ -4

3x + 2y ≤ -5

Step-by-step explanation:

it was right on plato

Answer:

G'(-3, -2), E'(1, 1), W'(-3, 0)

Step-by-step explanation:

A point has coordinates (x, y).

A translation of h units to the right means add h to x.

A translation of h units to the left means subtract h from x.

A translation of k units up means add k to y.

A translation of k units down means subtract k from y.

The translation you need to do is 1 unit right and 2 units down.

That means add add 1 to x of each point. Subtract 2 from y of each point.

G(-4, 0) ----> G'(-4 + 1, 0 - 2) = G'(-3, -2)

E(0, 3) ----> E'(0 + 1, 3 - 2) = E'(1, 1)

W(-4, 2) ----> W'(-4 + 1, 2 - 2) = W'(-3, 0)

Answer:

$1,800

Step-by-step explanation:

We know that Tamara invested $15,000 and gets %4 of it each year, She plans to withdraw all the money by the end of 3 years.

4 percent of 15,000 is 600

So we can multiply 600 by three and add it to the 15,000

That gives us 16,800

So Tamara will make a $1,800 interest

Answer:

[tex]\bold{ 9x = (x+35)\times 5 }[/tex]

Step-by-step explanation:

Jim completed half of the floor in 9 hours.

Let the rate of Jim = [tex]x[/tex] tiles/hr

So, number of tiles that Jim lays in 9 hours = Rate of Jim multiplied by number of hours i.e. [tex]9 \times x[/tex] ..... (1)

Let [tex]y[/tex] tiles/hr be the rate at which Pete lays the tiles.

As per the given question, Pete can lay 35 more tiles per hour than Jim.

i.e. [tex]\bold{ y =x+35}[/tex]

It is given that half of the floor is done by Jim and other half by Pete.

So, we can say that number of tiles for both of them are equal.

Number of tiles by Pete = Rate of Pete [tex]\times[/tex] Number of hours = [tex](x+35) \times 5[/tex]...(2)

Now, we can equate the equations (1) and (2) because the number of tiles are same.

i.e.

The equation that we can use is:

[tex]\bold{ 9x = (x+35)\times 5 }[/tex]

Hi there! Hopefully this helps!

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|[tex](a^{3} - 2a^{2}) - (3a^{2} - 4a^{3} )[/tex]

|

| To find the opposite of [tex]3a^{2} -4a^{3}[/tex], find the opposite of each term.

\/

[tex]a^{3} - 2a^{2} - 3a^{2} + 4a^{3}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

|

|Combine [tex]-2a^{2}[/tex] and [tex]-3a^{2}[/tex] to get [tex]-5a^{2}[/tex].

\/

[tex]a^{3} - 5a^{2} + 4a^{3}[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

|

|Combine [tex]a^{3}[/tex] and [tex]4a^{3}[/tex] to get [tex]5a^{3}[/tex].

\/

Answer:

(6,2)

Step-by-step explanation:

The question is missing alternatives. The complete question is here.

For each student in a certain class, a teacher adjusted the student's test score using the formula y = 0.8x + 20, where x is the student's original test score and y is the student's adjusted test score. If the standard deviation of the original test scores of the students in the class was 20, what was the standard deviation of the adjusted test scores of the students in the class?

A. 12

B. 16

C. 28

D. 36

E. 40

Answer: B. 16

Step-by-step explanation: If you add a constant to each number at the data set, standard deviation doesn't change. However, multiplying each data in the data set by a constant, also multiplies the standard deviation by that constant.

That being said, the formulafor the adjusted test score is

y = 0.8x + 20

Adding 20 to each data doesn't change standard deviation but multiplying by 0.8 changes it.

So, the new standard deviation is

σ = 20*0.8 = 16

Standard Deviation for the adjusted test scores of the students is 16.

Answer:

The coordinates of the point at 3/4 of the distance from A to B from A is (-3.5, 1.25)

Step-by-step explanation:

The coordinates of the point A is (-5, -4),

The coordinates of the point B is (-3, 3)

Let the point 3/4 from A to B = P

The coordinates of the point 3/4 from A to B is found as follows;

(-5 + (3/4×(-3 - (-5)), -4 + 3/4×(3 - (-4)) which gives;

The coordinates of the point 3/4 from A to B as P(-3.5, 1.25)

We verify the length from A to B  and from A to P as follows;

The distance l between two points (x₁, y₁) and  (x₂, y₂) is given by the formula;

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

For AB, we have;

[tex]Length \ of \ segment \ \overline {AB} = \sqrt{\left (3-(-4) \right )^{2}+\left ((-3)-(-5) \right )^{2}}=\sqrt{53} \approx 7.28[/tex]

[tex]Length \ of \ segment \ \overline {AP} = \sqrt{\left (1.25-(-4) \right )^{2}+\left ((-3.5)-(-5) \right )^{2}}= \dfrac{3}{4} \cdot \sqrt{53}[/tex]

Therefore, the point P (-3.5, 1.25) is the point 3/4 distance of A to B from A.

Identifying the distance and applying the fraction, it is found that the coordinates are (-3.5, 1.25).

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

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

[tex]x = -5 + 2\frac{3}{4} = -5 + \frac{6}{4} = -\frac{20}{4} + \frac{6}{4} = -\frac{14}{4} = -\frac{7}{2} = -3.5[/tex]

[tex]y = -4 + 7\frac{3}{4} = -4 + \frac{21}{4} = -\frac{16}{4} + \frac{21}{4} = \frac{5}{4} = 1.25[/tex]

The coordinates are (-3.5, 1.25).

A similar problem is given at https://brainly.com/question/24647154

Answer:

4√(xy³)

Step-by-step explanation:

8√(x²y⁶)

The above expression can be simplified as follow:

8√(x²y⁶)

Recall:

m√a = a^1/m

Therefore,

8√(x²y⁶) = (x²y⁶)^1/8

Recall:

(aⁿ)^1/m = a^(n/m)

Therefore,

(x²y⁶)^1/8 = x^(2/8)•y^(6/8)

= x^1/4•y^3/4

= (xy³)^1/4

Recall :

a^1/m = m√a

Therefore,

(xy³)^1/4 = 4√(xy³)

Therefore,

8√(x²y⁶) = 4√(xy³)

Step-by-step explanation:

Answer:

3√6

Step-by-step explanation:

[tex] {a}^{2} = {b}^{2} + {c}^{2} [/tex]

[tex] = {1}^{2} + {( \sqrt{53} )}^{2} [/tex]

[tex] = 1 + 53[/tex]

[tex] {a}^{2} = 54[/tex]

[tex]a = \sqrt{54} = 3 \sqrt{6} [/tex]

Answer:

Step-by-step explanation:

[tex]7x+6<3\left(x-2\right)\\\\\mathrm{Expand\:}3\left(x-2\right):\quad 3x-6\\\\7x+6<3x-6\\\\\mathrm{Subtract\:}6\mathrm{\:from\:both\:sides}\\\\7x+6-6<3x-6-6\\\\Simplify\\\\7x<3x-12\\\\\mathrm{Subtract\:}3x\mathrm{\:from\:both\:sides}\\\\7x-3x<3x-12-3x\\\\\mathrm{Simplify}\\\\4x<-12\\\\\mathrm{Divide\:both\:sides\:by\:}4\\\\\frac{4x}{4}<\frac{-12}{4}\\\\x<-3[/tex]

Assuming you misspelled thousandths:

Answer:

67.401

Step-by-step explanation:

0.000 <- this is the thousandths place

5 is greater than or equal to 5, which means you round up.

0+1 = 1.

Answer:

C

Step-by-step explanation:

When completing the square, we essentially want to create a perfect square trinomial by adding a constant.

If we have the following expression:

[tex]x^2+bx[/tex]

And we want to complete the square, we will need to divide the b-coefficient by half and then square it.

Thus, the added term should be:

[tex](b/2)^2[/tex]

In the given equation, we have:

[tex](x^2-8x)-10[/tex]

The b term here is 8. Therefore:

[tex](8/2)^2\\=(4)^2\\=16[/tex]

The value we would add would be 16.

The answer is C.

Further notes:

To complete the square, add 16 like mentioned earlier. However, we also need to subtract 16 to balance things out:

[tex](x^2-8x)-10\\=(x^2-8x+16)-10-16\\[/tex]

The expression inside the parentheses is now a perfect square trinomial. Factor it:

[tex]=((x)^2-2(4)(x)+(4)^2)-26\\=(x-4)^2-26[/tex]

And we are done!

A quadratic function equation is as follows:

[tex]ax^{2} + bx + c[/tex]

To complete the square, move the constant (c) to the other side of the equation and take half of the b value, square it, and add and subtract the same number.

In this problem, you will add 16.

[tex] \frac{ - 8}{2} = - 4[/tex]

[tex] - 4^{2} = 16[/tex]

Answer:

x≥-56

Step-by-step explanation:

[tex]-12\le \:44+x\\44+x\ge \:-12\\\mathrm{Subtract\:}44\mathrm{\:from\:both\:sides}\\44+x-44\ge \:-12-44\\x\ge \:-56[/tex]