1. In a 30-60-90 triangle, the length of the hypotenuse is 6. What is the length of the shortest side?



A2
B3
C \(3\sqrt{2}\)
D\(3\sqrt{3}\)
F\(6\sqrt{2}\)

Answer:

15.3 gallons

Step-by-step explanation:

We can write a ratio

420 miles      357 miles

--------------  = --------------

18 gallons    x gallon

Using cross products

420x = 357*18

420x =6426

Divide each side by 420

420x/420 = 6426/420

x =15.3

Answer:

2/7

Step-by-step explanation:

got 100%

Answer:

B. 1 1/12

Step-by-step explanation:

You're welcome

The equation of the line in slope-intercept form is y = 3x + 4.

We can use the combination formula to determine how many different packages can be created from a set of 24 crayons with 36 different colours.

The formula for the mixture is provided by:

n C r equals n!/r! (n-r)!

where r is the number of items we want to choose, n is the total number of items, and! stands for the factorial of a number, which is the sum of all positive integers up to that number.

In this instance, we are trying to determine how many various methods there are to choose 24 crayons from a set of 36 colours, regardless of the sequence in which they are chosen. Consequently, we can apply the following combination formula:

36 C 24 = 36! / (24! * 12!)

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Let's assume David's average speed is S km/h.

A) To find David's average speed, we can use the formula: Speed = Distance / Time.

David completed the race in 5 hours, so his speed is S km/h. Therefore, we have:

S = Distance / 5

B) Ken's average speed is 9.8 km/h less than David's average speed, which means Ken's average speed is (S - 9.8) km/h.

Ken took 7 hours to complete the race, so we have:

S - 9.8 = Distance / 7

Now, we can solve the system of equations to find the values of S and Distance.

From equation (1): S = Distance / 5

Substitute this into equation (2):

Distance / 5 - 9.8 = Distance / 7

Multiply both sides of the equation by 35 to eliminate the denominators:

7 * Distance - 35 * 9.8 = 5 * Distance

7 * Distance - 343 = 5 * Distance

Subtract 5 * Distance from both sides:

2 * Distance - 343 = 0

Add 343 to both sides:

2 * Distance = 343

Divide both sides by 2:

Distance = 343 / 2 = 171.5 km

Therefore, the distance of the cycling race is 171.5 kilometers.

To find David's average speed, substitute the distance into equation (1):

S = Distance / 5 = 171.5 / 5 = 34.3 km/h

So, David's average speed was 34.3 km/h.\(\)

Answer:

A) 34.3 km/h

B) 171.5 km

Step-by-step explanation:

Since Ken's average speed is said to be 9.8km/h less than David's average speed, and we know that Ken's average speed is dependent on him traveling for 7 hours, then we have our equation to get the distance of the cycling race:

\(\text{Ken's Avg. Speed}=\text{David's Avg. Speed}\,-\,9.8\\\\\frac{\text{Distance}}{7}=\frac{\text{Distance}}{5}-9.8\\\\\frac{5(\text{Distance})}{7}=\text{Distance}-49\\\\5(\text{Distance})=7(\text{Distance})-343\\\\-2(\text{Distance})=-343\\\\\text{Distance}=171.5\text{ km}\)

This distance for the cycling race can now be used to determine David's average speed:

\(\text{David's Avg. Speed}=\frac{\text{Distance}}{5}=\frac{171.5}{5}=34.3\text{ km/h}\)

Therefore, David's average speed was 34.3 km/h and the distance of the cycling race was 171.5 km.

Answer:

Step-by-step explanation:

11*1.8*\(10^{-8} =19.8*10^{-8} =1.98*10^{-9}\)

The perimeter of the given window is 48 centimeter.

From the given figure,

Perimeter of window = 2(Length+Breadth)

= 2(10+14)

= 2×24

= 48 centimeter

Perimeter of house = 2(Length+Breadth)

= 2(37+35)

= 2×72

= 144 centimeter

Perimeter of roof = 2(Length+Breadth)

= 2(37+5)

= 2×42

= 84 centimeter

Therefore, the perimeter of the given window is 48 centimeter.

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Answer:

xy-y^2/x

Step-by-step explanation:

you factor the expression and reduce the gcf 3:

(x-y)*(x+y)/x *y/x+y

reduce the expression with x+y:

x-y/x*y

calculate the product:

y*(x-y)/x

remove parenthesis:

xy-y^2/x

Answer:

a i guess there isnt a queston here

Step-by-step explanation:

Answer: hello there! the answer is a. <A ≅ <A; reflexive property, hope this helps :)

Step-by-step explanation: i just completed the unit practice test and got 100%

Answer:

7: 113.1 yd

In terms of Pi: 36π

8: 326.85 in

In terms of Pi: 104π

6: 452.39 km

In terms of Pi: 144π

Step-by-step explanation:

Answer:a car

Step-by-step explanation:

The computation shows that 6 × 5000 = 3000.

Based on the information given, the steps to put in the box will be

Step 1. 6×5×1000

Step 2. 30×1000

Step 3. 30,000

Therefore, the computation shows that 6 × 5000 = 3000.

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Fill in the blanks to solve 6 x 5,000.

6 x 5,000

Step 1. 6 x 5 x __

Step 2. 30 x __

Step 3. __

The standard form of the equation of the line passing through (8,-3) that is parallel to the line 3y=4x+8 is 4x - 3y = 41

The equation of the line in standard form can be represented as follows:

Ax + By = C

where

Therefore, the standard form of the equation of the line through (8,-3) that is parallel to the line 3y = 4x + 8 is a s follows;

Parallel lines have the same slope.

Hence,

3y = 4x + 8

y = 4  / 3 x + 8 / 3

The slope of the line is 4 / 3. Hence, the line passes through (8, -3). let's find the y-intercept.

y = 4 / 3 x + b

-3 = 4 / 3 (8) + b

b = -3 - 32 / 3

b =  -9 - 32/ 3

b = -41 / 3

Hence,

y = 4 / 3 x - 41 / 3

multiply through by 3

3y = 4x - 41

Therefore, the standard form is 4x - 3y = 41

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Answer:16

Step-by-step explanation:

Given: 15% of 60 is 9.

so 9 kids are 15 year old.

and 1 other kid is 16 year old.

Thus, there are total of (15+1) kids that are either 15 or 16 year old. you can also draw venn diagram to find that.

Answer: 3/5 (0.6 decimal form)

Step-by-step explanation:

Answer:

Step-by-step explanation:

The bell boy added $270 and $20 incorrectly. The $20 bill was something that was returned due to overcharching. On the other hand, $270 was the amount that they paid for their room. This only means that $20 should be deducted from $270 and that's the amount that they paid for their room while $30 and $20 are the amount that the bell boy received as a tip

Total money of the three men: 3($100) = $300

They paid $270 for the room: $300 - $270 = $30

Tip for the bell boy: $30 - $30 = $0

Amount overcharged to them: $0 + $20 = $20

Tip to the bell boy: $20 - $20 = $0

They were left with no more money from the original $300.

Answer:

H= 2x+3

brainliest please :)

The value of ∠H will be -6x +4 for the given figure.

Geometry is one of the oldest branches of mathematics, along with arithmetic. It is concerned with spatial properties such as figure distance, shape, size, and relative position.

Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.

The angle will be calculated as,

∠H + 3x - 10 + 3x + 6 - 180 + 180 = 0

∠H +6x -4 = 0

∠H = -6x + 4

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Answer:

6

Step-by-step explanation:

The two triangles are similar which means the the two length is parallel

.°., the Length of the smaller triangle=6

The number of soda bottles the machine can make per minute is 25

From the question, we have the following parameters that can be used in our computation:

The linear relation

Where we have the points

(2, 50) (6, 150)

A linear equation is represented as

y = mx + c

Where

c = y when x = 0

m = unit rate i.e the required slope

So, we have

2m + c = 50

6m + c = 150

Next, we have

4m = 100

Evaluate

m = 25

So, we have

2 * 25 + c = 50

Evaluate

c  0

So, we have

y = 25x

Hence, the equation of the line in fully simplified slope-intercept form is y = 25x

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Answer:

20

Step-by-step explanation:

Answer:

Becky is 7 years old.

Step-by-step explanation: Let b - Becky's age ; Equation - 3b = 21. Divide both size by 3 to isolate the variable.

Answer:

Becky's 7 seven years old

Step-by-step explanation:

If 21 = 3x

x = 21/3

x = 7

Hope this helps :)

Pls brainliest...

On each roll of a 6-sided die, we have 6 possible outcomes.

Then if we roll it twice, we will have 36 outcomes.

The outcomes where the sum is 4 are:

roll 1     roll 2    sum

1             3           4

3            1            4

2           2           4

Son in 3 out of 36 outcomes the sum can be 4, then the probability opf rolling a sum of 4 is given by the quotient:

P = 3/36

P = 1/12

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Answer:

i believe _=6 (the horizontal side, as it says on the picture,) | = 6 (the vertical side,) and \ = 8.48 (the diagonal)

Step-by-step explanation:

To find the diagonal, you have to use the Pythagorean Theorem, which is a^2 + b^2 = c^2

So, a and b both equal 6, square both of those, you got 36 for each.

Now, add them together and youll get 72

The square root of 72 is around 8.48

Although, im not entirely sure if thats correct or not, so i wouldnt really recommend putting this as your answer :|

Hey there! :)

Answer:

A. 23.

Step-by-step explanation:

Given:

5 + 2(x + 7)² for x = -4

Substitute in -4 for x in the equation:

5 + 2((-4) + 7)²

5 + 2(3)²

5 + 2(9)

5 + 18 = 23.

Therefore, the correct answer is A. 23.

Answer:

23

Step-by-step explanation:

5 + 2(x + 7)^2

Let x =-4

5 + 2 ( -4+7)^2

Parentheses first

5 +2 (3)^2

5+ 2*9

Multiply

5+18

add

23

Answer:

D

Step-by-step explanation:

Answer:

It would be A

Step-by-step explanation:

Step 1

Polynomials are algebraic expressions that consist of variables and coefficients.

An example of a polynomial with one variable is;

All the exponents in the algebraic expression of a polynomial must be non-negative integers in order for the algebraic expression to be a polynomial. As a general rule of thumb if an algebraic expression has a radical in it then it isn’t a polynomial.

The given question is;

Answer;

This is because of the radical in the power of the x with a coefficient of 3.

Using slope formulas, we can conclude that Lydia's assertion is incorrect.

The coordinates of the triangle are given as:

\(D = (- 2, - 1)\)

\(E= (- 2, 2)\)

\(F =(0, 0)\)

Start by calculating the slopes of lines DF and EF using the following slope formula

\(m = \frac{y_2 -y_1}{x_2 -x_1}\)

So, we have:

\(m_{DF} = \frac{-1 -0}{-2 -0}\)

\(m_{DF} = \frac{1}{2}\)

Next, we calculate the slope of EF

\(m_{EF} = \frac{2 - 0}{-2 - 0}\)

\(m_{EF} = -1\)

For the triangle to be a right-angled, the following must be true

\(m_{EF} \times m_{DF}= -1\)

So, we have:

\(-1 \times \frac 12= -1\)

\(-\frac 12= -1\)

The above equation is not true.

Hence, Lydia's assertion is incorrect.

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