The angles in a triangle are in the ratio 3:2:1.
a) Show that the triangle is a right-angled triangle
b) The hypotenuse of the triangle is 25 cm long.
Calculate the length of the shortest side in the triangle

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

(a)

sum the parts of the ratio, 3 + 2 + 1 = 6 parts

The sum of the 3 angles in a triangle = 180°  , then

180° ÷ 6 = 30° ← value of 1 part of the ratio , then

3 parts = 3 × 30° = 90°

2 parts = 2 × 30° = 60°

1 part = 30°

The angles in the triangle are 90°, 60°, 30°

Thus the triangle is right angled

(b)

The shortest side is opposite the smallest angle, that is opposite 30°

Using the sine ratio in the right triangle and the exact value

sin30° = [tex]\frac{1}{2}[/tex]

sin30° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{opposite}{25}[/tex] = [tex]\frac{1}{2}[/tex] ( cross- multiply )

2 × opposite = 25 ( divide both sides by 2 )

opposite = 12.5

That is shortest side is 12.5 cm


Related Questions

Identify the conclusion of the statement.
If AB is a segment, then it has two endpoints.



A. The segment has two endpoints.

B. If AB is a segment.

C. AB vis a segment.

D. Then, the segment has two endpoints.

Answers

Answer:

its b

Step-by-step explanation:

HELPS PLS DUE IN 5 min:( ILL MARK BRAINIEST!!!

Where is the magnetic field in a hair dryer

Answers

Answer:

Hi :)

ELF magnetic fields measured 10 cm from the nozzles of hair dryers were elevated over the ambient by a mean factor of 17 when these devices were in use. Estimated mean daily times of usage of hair dryers, stereo headsets, and sewing machines were 2.6, 19, and 17 minutes, respectively.

Hope this helped :)

what is the slope of (16,1) and (17,7)

Answers

6 or 6/1.

The slope formula is (y2-y1)/(x2-x1). Replace the formula with the actual numbers. You should have 7-1/17-16. After subtracting, you will have 6/1, which is equal to 6. Hope that helped!

What is the value of x?

Answers

Answer:

sine 60 = x / 8

(8 * 0.86603) = x

x = 6.92824

Step-by-step explanation:

If a number is multiplied by 2/5, the product is (great than, less than, or equal to,) the number

Answers

Answer:

less than

Step-by-step explanation:

it's a fraction, so it will be a fraction of the original number.

The equation y = -4X -1 Has a slope of _______ possible answer choices: -4,-1, no slope and 0) and a y-intercept of possible answer choices: -4, -1 0 and no y-intercept)_______?

Answers

Answer:

slope = - 4 , y- intercept = - 1

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 4x - 1 ← is in slope- intercept form

with slope m = - 4 and y- intercept c = - 1

Answer:

-4 then -1

Step-by-step explanation:

The number behind the x value is the gradient and the last number is the y - intercept.

Sarah is paid $20 an hour at her new job. She wishes to graph her total pay y, as a function of the
number of hours, x. She wants to be sure her graph shows her pay for 10 and 20 hours of work.

Answers

Answer:

see image; 200; 400

Step-by-step explanation:

y=20x

graph

You want to buy some noodles. A 6-ounce package costs $1.92. A 14-ounce package costs $4.62
A 20-ounce package costs $6.20. Which package is the best buy?



Answers

Answer:

The 20 ounce is the best package to buy.

Step-by-step explanation:

Divide the cost of the noodles by the ounces and you'll get your answers and then you have to pick the one with the least cost per noodles.

The 6 ounce costs .32 each

The 14 ounce costs .33 each

And the 20 ounce costs .31 each

How Many Solutions Does 6 + [tex]\frac{x}{5}[/tex] = [tex]\frac{x}{5}[/tex] - 5 - [tex]\frac{3x}{10}[/tex] Have?

A. One solution
B. Two solutions
C. No solutions
D. Infinitely many solutions

Answers

Answer:

A. One solution

Step-by-step explanation:

6 + x/5 = x/5 - 5 - 3x/10

Cancel equal terms on both sides.

6=-5-3x/10

Multiply both sides of the equation by 10.

60=-50-3x

Move the variable to the left-hand side and change the sign.

60+3x=-50

Move the constant to the right-hand side and change the sign.

3x=-50-60

Calculate the difference.

3x=-110

Divide both sides by 3.

x=-110/3

=-36 2/3

Meaning one solution.

Hope this helps :)

Answer:

The answer you are looking for is A

On the grid below, which point is located in the quadrant where the x-coordinate is a positive number and the y-coordinate is a negative number?
A coordinate plane is shown. Point A is in quadrant 1, point B is in quadrant 2, point C is in quadrant 3, and point D is in quadrant 4.
A
B
C
D

hurry!!

Answers

Answer:

The answer is A.......

Step-by-step explanation:

the diagonal of a cube is root 12. What is the edge?

Answers

Step-by-step explanation:

Given length of diagonal of a cube = √12 cm Recall that length of diagonal of a cube = √3 × Length of edge of the cube ⇒ √12 = √3 × Length of edge of the cube ∴ Length of edge of the cube = √12 / √3 = 2√3 / √3 = 2 Thus the edge of the given cube is 2 cm

A 5-pound bag of apples cost $3.50. Use that rate, to complete the table to identify equivalent ratios, and then answer the questions.

Apples cost $ __ per pound.
brainliest 100pts

Answers

Answer:

Cost 0.70 per pound.

Step-by-step explanation:

If you see the cost and the weight you can get the price per pound, so if 5 pounds cost $3.50, you can evaluate doing a rule of three:

So if you clear X you´d get this:

So the cost per pound is $0.70.

Now that you have the cost per pound you can do the equivalent ratios:

Cost---------------Apples

0.70---------------1 pound

3.5--------------- 5 pounds

 7---------------  10 pounds

Brainliest me bro

Answer:

70 cents per pound

Step-by-step explanation:

$3.50/5lb= 70 cent

40.8 divide by 12 pleas find it

Answers

Answer:

40.8 ÷ 12 = 3.4

Step-by-step explanation:

---------

The solution of expression 40.8 divide by 12 is, 3.4

The given numbers to divide are,

⇒ 40.8 divide by 12

Let us assume that, a is divided by b,

Then, it can be written as,

⇒ a / b

Hence, We can write as,

⇒ 40.8 / 12

⇒ 408 / 120

⇒ 3.4

Therefore, The solution of expression 40.8 divide by 12 is, 3.4

Learn more about the divide visit:

brainly.com/question/28119824

#SPJ6

Nine more than a number, divided by -4, is a
maximum of -2." I also need step by step explanation please if u can

Answers

Step-by-step explanation:

Let's use the number represented x

x + 9 because 9 more than the x

(x+9)/-4 because it is divided by -4

(x+9)/-4 <= -2 (maximum of -2 means smaller than -2, but it also did not tell not to use -2)

What is the greatest common factor of 50, 15, and 10?

Answers

Answer:

5

Step-by-step explanation:

you would need to factor each of the number and they are all in the 5 times table

Answer:

GCF = 5

Step-by-step explanation:

Reason being that all are divisible my 5 and 10 cannot be used because it makes a fraction which is not how the GCF can be found.

Math:

50 = 5 * 10 or 25 * 2 or 50 * 1

15 = 5 *3 or 15* 1

10 = 5 * 2 or 10 * 1

Only thing that is the same is 5, thus 5 is the GCF.

1 year = 12 months
3/4 year =

Answers

Answer:

3/4 year = 9

Step-by-step explanation:

To find 3/4 of a year you first need to find 1/4 of a year so you do 12/4 and get 3. Now we know that 1/4 of a year is 3 months so you just multiply that by 3 to get 9. So 3/4 of a  year is 9 months.

I hope this helps!

Your answer to 3/4 of a year is 9 months

Write the slope- intercept form of the equation

Answers

Answer:

y = -3/4x + 1

Step-by-step explanation:

What is the area (what is the height)

Answers

Answer:

5 i think

Step-by-step explanation:

The trapezoid's height (h) is 4 mm(millimeters).

Formula to calculate a trapezoid's height;

2 x Area ÷ by A(short base) + B(large base)

Use angle relationships to complete the top equation. Then, solve for x and find the measure of both angles.

Answers

7x + 5 = 180
x = 25
6x = 150
x + 5 = 30

Find 3 ratios that are equivalent to the given ratio 3 over 6

Answers

1/2 2/4 5/10 are also equivalent to the 3/6 ratio!!!

PLEASE HELP ME ILL
MARK BRAINLIEST

Answers

Answer:

yeah

Step-by-step explanation:

+ 1 x 4
2-
ax + b
can be written as a single fraction in the form
X2 x + 2
x² - 4
where a and b are integers.
x+ 2 x -
Work out the value of a and the value of b.

Answers

[tex]2 - \frac{x+1}{x-2} - \frac{x-4}{x+2} = \frac{2(x-2)(x+2)}{(x-2)(x+2)} - \frac{(x+1)(x+2)}{(x-2)(x+2)} - \frac{(x-4)(x-2)}{(x-2)(x+2)} \\= \frac{2(x-2)(x+2)-(x+1)(x+2)-(x-4)(x-2)}{(x-2)(x+2)} \\= \frac{2x^{2} -8-x^{2}-3x-2-x^{2} +6x-8 }{x^{2} -4} \\=\frac{3x+(-18)}{x^{2} -4}[/tex]

so : a = 3   b = -18

ok done. Thank to me :>

The kitchen of a house is of size 15ft x 12ft. Find the cost of tiling the wall at all sides 5 ft from the base at the rate of Rs. 120/sq ft.​

Answers

Answer:

20400RS

Step-by-step explanation:

Given, Kitchen Size = 15ft * 12ft wall height to be tiled = 5 ft so area of focer walls

= 2* 15+2*5*12

= 150+120=170ft.

Rate is 120/ sq*ft here rate

= 120*170

= 20400RS

Cereal is on sale this week. Is it a better buy to get the 10-ounce box for $2.12 or the 14-ounce box for $2.74?

Answers

First you want to know the price for each ounce. So for the 10 ounce box: 2.12 / 10= $0.212 per ounce. Now for the 14 ounce box : 2.74/ 14 = $0.19 per ounce. So the 14 ounce box is cheaper for $2.74 as 0.19<0.21

The 14-ounce box is cheaper at a cost of $2.74 than the 10-ounce box.

What is the division operation?

In mathematics, divides left-hand operands into right-hand operands in the division operation. The primary purpose of the division is to generate equal groupings or to determine how many people are in each category after a fair distribution.

For example 4/2 = 2

First, we have to find the price for each ounce.

So for the 10-ounce box:

⇒ 2.12 / 10

Apply the division operation,

⇒ $0.212 per ounce.

Now for the 14-ounce box:

⇒ 2.74/ 14

Apply the division operation,

⇒ $0.19 per ounce.

Here the cost of the 14-ounce box is less than the 10-ounce box as 0.19 < 0.21

Therefore, the 14-ounce box is cheaper at a cost of $2.74.

To learn more about the division operation click here :

brainly.com/question/25870256

#SPJ2

What is the constant of proportionality in the equation
Below

Answers

Answer:

k = 9/2

Step-by-step explanation:

Constant of proportionality, k = y/x

given: x/y = 2/9

since k = y/x, therefore, k value will now be inverse of 2/9, which is 9/2

Keenan worked at an ice cream shop. One day, he counted the first 8
flavors requested. Here are the results:
Ice Cream Flavors
Count
Flavor
peach
3
o
vanilla
chocolate
1
coffee
4
Supposing these trends continue, how many of the next 6 requests will
be for coffee?

Answers

Answer:

2

Step-by-step explanation:

correct me if i'm wrong

la la la

A SQUARE RECTANGULAR PRISM (BASE IS A SQUARE) HAS A
VOLUME OF 38 CU. IN. THE HEIGHT IS 10 LESS THAN THE AREA
OF THE BASE. WHAT IS THE HEIGHT? NO UNITS.

Answers

The height of the prism [tex]\approx 2.9[/tex]

The whole volume of the prism is

[tex]\text{Volume} = \text{Area of base}\times \text{Height}[/tex]

Here, the volume is 38 cu. in.

From the question, the area and the height are related as follows;

[tex]\text{Height} = \text{Area} - 10 \implies \text{Height + 10} =\text{Area}[/tex]

Substituting this into the formula for the volume, we get

[tex]\text{Volume}=(\text{Height} +10)\times \text{Height}=38\\\\\text{Height}^2 + 10\times\text{Height}=38\\\\\text{Height}^2 + 10\times\text{Height}-38=0[/tex]

If the above quadratic equation is solved for the height, we get

[tex]\text{Height}\approx 2.9[/tex]

(We can't take the other solution since height has to be greater than zero)

Another word problem on volume can be found in this link: https://brainly.com/question/17142547

A recipe for 2 dozen cookies uses 300 grams of flour, 250 grams of butter,
and 150 grams of sugar. How much of each ingredient would be required to make 120 cookies?
Flour:
grams
Butter:
grams
Sugar:
grams

Answers

Flour; 1500grams
Butter; 1750grams
Sugar;750 grams

(2.5×10^6)–(2.3×10^6)

Answers

Answer:

2×[tex]10^{5}[/tex]

aka 200000

Step-by-step explanation:

What is the domain and range of the function below

Answers

Domain is [+7,+infinity[
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