Find the greatest possible pair of numbers such that one integer is 5 more than twice the other and the sum is less than 30.

The length of the missing side = side B = 17 (D) or 51(A)

Triangles are flat fields bounded by 3 intersecting sides and 3 angles

This side can be the same length or different.

If at an angle there is an angle of 90 degrees, this triangle is said to be a right angle

There is a hypotenuse in this triangle which is the sum of the two sides

[tex]\large{\boxed{\bold{C^2=A^2+B^2}}[/tex]

where c = hypotenuse

a and b = side/leg

This formula is known as the Pythagorean theorem which states that:

the hypotenuse or the longest side in a right triangle equal to the sum of the squares of the other sides.

or

the sum of the squares of the length of the two sides equals the square of the length of the hypotenuse

While the angle formulas used are

From the problem it is known that side A = 38 ,side b = b, side c = 34

There are 2 possible solutions to this problem because the image does not exist:

Possible Solution no 1

A² = C²+B²(A=hypetenuse)

B² = A²-C²

B² = 38² - 34²

B² = 288

B = √288

B = 16.97, round to the nearest tenth ⇒ 17 (answer D)

Possible Solution no 2

B² = A²+C²(B=hypotenuse)

B² = 38² + 34²

B² = 2600

B = √2600

B = 50.99, round to the nearest tenth ⇒ 51 (answer A)

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Keywords: Pythagoras' theorem, the trigonometric, hypotenuse

Since we are given the lengths of 2 sides with the angle in between, therefore by cosine law we can only construct 1 triangle from this. By stating the angle in between, this constricts the possible number of triangles that can be formed into 1.

By calculation, the length of the 3rd side is calculated using cosine law:

c^2  = a^2 + b^2 – 2abcosθ

c^2 = 10^2 + 8^2 – 2(10)(8)cos40

c = 6.44 cm

ANSWER:

1 triangle 

The volume of the pyramid with a base area of 8 square units and a height of 16 units is 42.67 cubic units.

The volume of a pyramid is calculated as one-third of the base area times the height. The base area of the given pyramid is 8 square units and the height is 16 units. Using the formula for volume V =  rac{1}{3}Ah, where A is the base area and h is the height, the volume of the pyramid can be found as follows:

V =  rac{1}{3}  imes 8  imes 16

V =  rac{1}{3}  imes 128

V = 42.67 cubic units (rounded to two decimal places).

Therefore, the volume of the pyramid is 42.67 cubic units.

The answer is C. x = [tex]\frac{5}{2}[/tex] 0r x = [tex]\frac{1}{3}[/tex]

Answer:

21-y

Step-by-step explanation:

In mathematics the signs used for more than is + and for less than is -.

The question is asking us to write y less than 21 in mathematical statement form.

y less than 21 means 21-y,

Hence the mathematical statement for y less than 21 is 21-y.

Answer:

Option C.

Step-by-step explanation:

The given expression is ab - 2 = c

Option a : a = [tex]\frac{c}{b}[/tex] - 2

                 ab = c - 2b

                Not equivalent to the original expression.

Option b : b = c + [tex]\frac{2}{a}[/tex]

                 ab = ac + 2 ⇒  [tex](\frac{ab-2}{a})[/tex] = c

                Not equivalent

Option c  : ab = c + 2

                  ab - 2 = c

               Equivalent to original expression

Option d : a - [tex]\frac{c}{2}[/tex] = b

                 2a - c = 2b

                Not equivalent

Option e : b - [tex]\frac{2}{c}[/tex] = a

                 bc - 2 = ac ⇒ c (b-a) = 2 ⇒ c = [tex]\frac{2}{b-a}[/tex]

                 Not equivalent

Option f : a = c + [tex]\frac{2}{b}[/tex]

                ab = bc + 2

               [tex](\frac{ab-2}{b} )[/tex] = c

              Not equivalent

Vanilla wafers cost $4 per packet

and chocolate wafers for $1 per packet

They spent a total of $45 .

This means that the equation that can be formed using this information is:

                   4x+y=45

and they buy a total of 27 packets of wafers.

i.e.   the equation formed with the help of this information is:

              x+y=27

PART A:

The system of equations that can be solved to find the number of packets of vanilla wafers and the number of packets of chocolate wafers that Josh and his friends bought at the carnival is:

                 4x+y=45-------------------(1)

and             x+y=27----------------(2)

PART B:

We will use the method of substitution because with the help of this method we could easily substitute the value of one variable in terms of the other variable and obtain the answer.

Using equation (2) we have:

   y=27-x-------------------(3)

On putting this value of y in equation (1) we have:

4x+27-x=45

i.e.

4x-x+27=45

i.e.

3x+27=45

i.e.

3x=45-27

i.e.

3x=18

i.e.

x=6

and on putting the value of x in equation (3) we have:

y=27-6

i.e.   y=21

Hence, number of vanilla wafers purchased = 6

and number of chocolates wafers purchased = 21

Answer:

the sum of the measures of angle B and angle C will also be 128 degrees meaning that the sum will decrease by 24 degrees.