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2 years ago

Due very soon but I can buy myself some time.

Mathematics

1 answer:

34kurt2 years ago

7 0

Answer:

4) 16√3 in²

5) 63 cm²

Step-by-step explanation:

The formula to use in these cases is ...

A = (1/2)ab·sin(θ)

where a, b are the side lengths and θ is the angle between them.

It helps to know the trig functions of the "special" angles used here.

sin(120°) = sin(60°) = (√3)/2

cos(60°) = 1/2

sin(135°) = cos(45°) = (√2)/2

4) The external angle at the base is the supplement of 120°, so is 60°. Then the length of the missing segment between the end of the base and the right angle at h is ...

x = (8 in)cos(60°) = (8 in)(1/2) = 4 in

So, the bottom edge of the triangle is 12 in - 4 in = 8 in.

The area is ...

A = (1/2)(8 in)(8 in)sin(120°) = (1/2)64(√3)/2 in² = 16√3 in²

5) As in the previous problem, the difference between the given horizontal dimension and the base of the triangle is ...

x = (18 cm)cos(180°-135°) = 18(√2)/2 cm = 9√2 cm

Then the base of the triangle is ...

16√2 cm -9√2 cm = 7√2 cm

The area is then ...

A = (1/2)(18 cm)(7√2 cm)(√2)/2 = 63 cm²

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Find the length of "a", to<br> the nearest tenth, using<br> the Pythagorean Theorem.<br> Enter

bearhunter [10]

Answer:

$\sqrt{28} \approx 5.3$

Step-by-step explanation:

The Pythagorean Theorem says if you have a right triangle, then relationship between the three sides is the sum of the square of each leg is the hypotenuse squared.

So $a^2+b^2=c^2$

where a and b are legs and c is the hypotenuse.

Plug in your a,b, and c. In this case it is a,6, and 8.

This means we have

$a^2+6^2=8^2$

Simplify where you can before we begin the solving (the moving around of things to other sides).

$a^2+36=64$

Now time for the solving. We are first going to get $a^2$ by itself.

To do this, we just need to subtract 36 on both sides giving us:

$a^2=64-36$

$a^2=28$

Now to get rid of the square on a, just square root both sides:

$a=\sqrt{28}$ .

8 0

3 years ago

Write the quadratic equation whose roots are 1 and 5, and whose leading coefficient is 2.

Deffense [45]

Answer:

$\Large \boxed{\sf \bf 2x^2-12x+10}$

Step-by-step explanation:

Hello,

As 1 and 5 are roots we can write, with a real number, the quadratic equation as

a(x-1)(x-5)

and as the leading coefficient is 2 then a = 2

It comes

$2(x-1)(x-5)=2(x^2-6x+5)=2x^2-12x+10$

Thanks

8 0

3 years ago

Help me with this problem please

lions [1.4K]

3 circles are shown split into halves

so there are 6 halves (1/2) total

2 are fully colored and 1/2 of the 3rd is colored

so as a fraction it would be 5/6 ( 5 out of 6 halves are colored)

mixed number = 2 1/2 ( 2 and 1/2 circles are colored)

decimal would be 5/6 = 0.833

8 0

3 years ago

Two forces act on an object. The first Force has a magnitude of 400 Newtons and acts at an angle of 30 degrees as measured from

Sedaia [141]

ANSWER

Option D is correct

EXPLANATION

We resolve the forces into component forms.

$F_1 = 400 \cos(30) i + 400 \sin(30) j$

$F_1 = 200 \sqrt{3} i +200j$

Also the second is resolved to obtain,

$F_2= 280 \cos(135) i + 280 \sin(135) j.$

$F_2= - 140 \sqrt{2} i + 140 \sqrt{2} j$

To find the resultant vector, V, We add the corresponding components of the two forces to get:

$V=F_1+F_2$

$\implies \: V = (200 \sqrt{3} - 140 \sqrt{2} )i + (200 + 140 \sqrt{2})j$

The correct answer is D.

3 0

3 years ago

The tallest living man at one time had a height of 262 cm. The shortest living man at that time had a height of 68.6 cm. Heights

AysviL [449]

Answer:

more the z-score more will be the extreme. therefore tallest man has high extreme

Step-by-step explanation:

Formula for z-score: $\frac{X-\mu }{\sigma}$

where

X is height of tallest man

μ mean height

σ is standard deviation

z score for tallest is

z-score = $\frac{ 262 - 175.32}{8.17} = 10.60$

similarly for shortest man

z-score = $\frac{68.6 - 175.32}{8.17} = - 13.06$

more the z-score more will be the extreme. therefore tallest man has high extreme

6 0

3 years ago

Read 2 more answers