How many unique triangles can be made when one angle measures 90° and another angle is half that measure? 1 2 More than 2 None

Answer:

We use cosine rule also called cosine law which states

c^2=a^2+b^2-2abcosC

given

a=8cm, b=7cm, c=9cm cos C?

9^2=8^+7^2-2*8*7 cos C

expand

81=64+49-112 cos C

like terms together

81-113=-112 cos C

-32=-112cos C

multiply both sides by -1

32=112cos C

divide both sides by 112

32/112=cos C

cosC=0.2857

find cos inverse of 0.2857

angle C= 73.40

Answer:

- 920

Step-by-step explanation:

There is a common difference d between consecutive terms in the sequence, that is

d = 22- 30 = 14 - 22 = 6 - 14 = - 8

This indicates the sequence is arithmetic with sum to n terms given by

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2a₁ + (n - 1)d ]

where a₁ is the first term and d the common difference

Here a₁ = 30 and d = - 8 , thus

[tex]S_{20}[/tex] = [tex]\frac{20}{2}[/tex] [ (2 × 30) + (19 × - 8) ]

     = 10(60 - 152)

     = 10 × - 92

     = - 920

Answer:

8

Step-by-step explanation:

2n

Let n =4

2*4

8

Answer:

8

Step-by-step explanation:

= 2 * 4 (we know that n = 4)

= 8

Hope this helps!

Answer:

35 ft

Step-by-step explanation:

The arch is in the shape of a semicircle.

The distance around the arch is about 110 feet. This is the same as the circumference of the arch.

The height of the arch is the radius of the arch.

The circumference of a semicircle is given as:

[tex]C = \pi r[/tex]

where r = radius

Therefore:

110 = πr

=> r = 110/π

r = 35.01 ft ≅ 35 ft

The height of the arch is 35 ft

The height of the arch in feet is 35 ft.

Since The distance around the arch is about 110 feet.

We know that

The circumference of a semicircle should be

110 = πr

[tex]r = 110/\pi[/tex]

r = 35.01 ft

≅ 35 ft

hence, we can conclude that The height of the arch in feet is 35 ft.

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Answer:

$4/ hour

Step-by-step explanation:

every hour you go you add 4 dollars

example: 1 hour is $2

                2 hours is $6

Answer:

4 hours

Step-by-step explanation:

20-5x=0

5x= 20

x=4 hours

Answer:

Step-by-step explanation:

The key here is knowing that the equation of the line that passes through these points is same

Thus having (6,14) and (0,0), the slope is as follows;

m = y2-y1/x2-x1 = 0-14/0-6 = -14/-6 = 7/3

Now we can use this slope here to get the value of y in the question

All we need to do is tie write the equation of the line for between the points (6,14) and (2,y)

That would be;

7/3 = y-14/1-6

7/3 = y-14/-5

cross multiply;

-35 = 3(y-14)

-35 = -3y + 42

-3y = -35-42

-3y= -77

y = -77/3

y = 77/3

Answer:

C. 5.4

Step-by-step explanation:

Range means highest number minus lowest number.

7.5 - 2.1 = 5.4

[tex]answer =5.4 \\ given \: data = 2.1 , 2.6 , 7.2 , 5.5 ,4.1 , 5.5 ,7.5 , 6.1 \\ range = highest \: score - lowest \: score \\ \: \: \: \: \: \: \: \: = \: 7.5 - 2.1 \\ \: \: \: \: \: = 5.4 \\ hope \: it \: helps \\ good \: luck \: on \: your \: assignment[/tex]

Answer:

730864

Step-by-step explanation:

654321 +76543=730864

Answer:

216 cm^3

Step-by-step explanation:

Volume of a cube=s^3

6 cm^3=216 cm^3

Answer:

hope this helps you

Answer:

6.8

How many 6's can go into 40?

6 + 6 + 6 + 6 + 6 + 6 = 36

6 6's

Subtract the amount off

40.8-36=4.8

How many 6's can go into 4.8?

0.6 + 0.6 +0. 6 + 0.6 + 0.6 + 0.6 + 0.6 + 0.6 = 48

0.8 6's

4.8 = 4.8 = 0

6 6's + 0.8 6's = 6.8 6's

6.8 is the answer

If you have any questions you can ask

Step-by-step explanation:

Answer:

2

Step-by-step explanation:

Add the students that take math and physics and subtract the ones that take both so that they are not double counted

65+43-10 =98

There are 100 students

100-98 =2

There are 2 that take neither math nor physics

Answer:

You should be right

Step-by-step explanation:

Srry if I am wrong though

Answer:

The answer is D.

Step-by-step explanation:

Given that f(x) = g(x) which means that both functions intersect to each other. By looking at the graph, x = -2 or 0 or 2 are the places where they intersect.

[tex]answer \\ 71xy - 56x + 27y \\ solution \\ 7x(5y - 8) + 3y(12x + 9) \\ = 35xy - 56x + 36xy + 27y \\ combine \: like \: terms \\ = 35xy + 36xy - 56x + 27y \\ = 71xy - 56x + 27y \\ hope \: it \: helps[/tex]

Answer:

[tex] = 71xy - 56x + 27 \\ [/tex]

Step-by-step explanation:

[tex]7x(5y - 8 )+ 3y(12x + 9) \\ 35xy - 56x + 36xy + 27 \\ 35xy + 36xy - 56x + 27 \\ = 71xy - 56x + 27[/tex]

hope this helps

Answer:

slope = - 5

Step-by-step explanation:

Calculate the slope m using the slope formula

m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]

with (x₁, y₁ ) = (0, 2) and (x₂, y₂ ) = (2, - 8)

m = [tex]\frac{-8-2}{2-0}[/tex] = [tex]\frac{-10}{2}[/tex] = - 5

The value of the gradient is -1/5.

In order to find the gradient of a line either of the two ways can be used. First, the equation of line should be written in terms of y, then the coefficient of x is the gradient.

The other method is to find the two points on the graph and then take the ratio of the difference of corresponding coordinates.

The given points are (0,2) and (2,-8).

Since the gradient of the line segment between points (x₁, y₁) and (x₂, y₂) is given as,

Gradient = (y₂-y₁)/(x₂-x₁)

Substitute the corresponding values to obtain,

Gradient = (2-0)/(-8-2)

               = -2/10

               = -1/5

Hence, the gradient of the line segment joining the points (0,2) and (2,-8) is -1/5.

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Answer:

Let the first trip be x

Second trip is 2x-4

Third trip is 2(2x-4)

Fourth trip is 3x + 18

x + (2x-4) + 2(2x-4)+3x+18 = 426

x + 2x -4 + 4x - 8 + 3x + 18 = 426

10x + 6 = 426

10x = 426-6

x = 420/10 = 42 km

Second trip was

2x-4 = 2(42)-4 = 84-4 = 80 km

Third trip was

2 * 80 = 160 km

Fourth trip was

3(42) + 18 = 144 km

Answer:

t =1

Step-by-step explanation:

3t - 18 = 4(-3-3/4t)

Distribute

3t - 18 = -12 -3t

Add 3t to each side

3t -18+3t = -12 -3t+3t

6t -18 =-12

Add 18

6t -18+18 = -12+18

6t = 6

Divide by 6

6t/6 = 6/6

t =1

Answer:

t = 1

Step-by-step explanation:

start by distributing the 4 to whats in the parentheses.

4 (-3 - 3/4t)

-12 - 3t

*helpful tip: if you multiply a fraction by its denominator the product is equal to its numerator

now you have:

3t - 18 = -12 - 3t

add 18 to both sides

3t = 6 - 3t

add 3t to both sides

6t = 6

divide both sides by 6

t = 1

Answer:

1

Step-by-step explanation:

500/500=1

x / x = 1

Answer:

Step-by-step explanation:

This is because when you divide a number with each other then they cancel out to equal 1. This can happen with the letter x. So, x/x = 1.

Going back to the question 500/500 can cancel out to become 1.

Answer:

B

Step-by-step explanation:

Because you subtract 14 from the right and left of the = sign

and now we add one on tbe right and left of the = sign. so the quadratic problem would be 3x^2 + 9x -13

Answer:

2/5.

Step-by-step explanation:

1/4 / 5/8

= 1/4 * 8/5

= 1*8 / 4*5

= 8/20

= 2/5.

Answer:

Step-by-step explanation:

6 more than a number is 36: x+6=36

36 more than a number is 6: x+36=6

6 times a number is 36: 6x=36

Answer:

3:1

Step-by-step explanation:

Since there are 3 times more blue favorite kids, the ratio is

3:1

The ratio of the number of students who said blue to the number of students who said green is 3 : 1.

The ratio is a numerical relationship between two values that demonstrates how frequently one value contains or is contained within another.

Given:

Mark asked each student in a class to name their favorite color.

For this class,

the number of students who said blue is three times the number of students who said green.

Let n be the number of students who said green.

Then, 3n, the number of students who said blue.

The ratio of the number of students who said blue to the number of students who said green.

= 3n/ n

= 3/1

= 3: 1.

Therefore, the ratio is 3 : 1.

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Answer:

x = 2 or x = -2

Step-by-step explanation:

5x² - 15 = 5​

⇌

5x² = 15 + 5

⇌

5x² = 20

⇌

x² = 20/5 = 4

⇌

x² = 2²

⇌

x² - 2² = 0

⇌

(x - 2)(x + 2) = 0

⇌   we use the zero product property

x - 2 = 0 or x + 2 = 0

⇌

x = 2 or x = -2

Answer:

see below

Step-by-step explanation:

f(x) = x^2 – 2x – 3

To find the roots, set the equation equal to zero

0  = x^2 – 2x – 3

Factor, what two numbers multiply to -3 and add to -2

-3 * 1 = -3

-3 + 1 = -2

0 = (x-3)( x+1)

Using the zero product property

x-3 =0   x+1 =0

x=3          x=-1

Answer:

3

Step-by-step explanation:

cuz i said so lol

Answer:

613.5 m^2

Step-by-step explanation:

The area of the base is

A = 1/2 bh

   = 1/2 (10) (8.7) =43.5 m^2

We have three sides with all the same area

The area of one side is 10 * 16 = 160

3 * 160 = 480 m^2

Now to the top

We have 3 sides with the same area

The area of one side

A = 1/2 bh

A = 1/2 (10) (6)

   = 30 m^2

3* 30 = 90

Add all the areas together to get the total surface area

43.5 m^2+ 480 m^2 + 90 m^2

613.5 m^2

Answer:

[tex]\Huge \boxed{\mathrm{613.5 \ m^2 }}[/tex]

[tex]\rule[225]{225}{2}[/tex]

Step-by-step explanation:

We can find the total surface area by adding the surface area of the triangular prism with the surface area of the triangular pyramid at the top.

Surface area of the triangular prism:

10 × 8.7 × 1/2 + 16 × 10 × 3

⇒ 523.5

Surface area of the triangular pyramid:

6 × 10 × 1/2 × 3

⇒ 90

Adding the surface areas:

523.5 + 90

⇒ 613.5

[tex]\rule[225]{225}{2}[/tex]