MATHEMATICS HIGH SCHOOL

What is the measure of the vertex angle in the next triangle in the pattern?4 isosceles triangles in a row, each smaller than the one before. The first has base angles 89 degrees and vertex angle 2 degrees, the second has base angles 88 degrees and vertex angle 4 degrees, the third has base angles 87 degrees and vertex angle 6 degrees, and the fourth has base angles 86 degrees and vertex angle 8 degrees,

Not to scale

vertex angle =

Answers

Answer 1

Answer:

Answer:

The measure of the vertex angle of the next isosceles triangle is 10°

Step-by-step explanation:

The given information are;

The first isosceles triangle; Base angles = 89°, vertex angle = 2°

The second isosceles triangle; Base angles = 88°, vertex angle = 4°

The third isosceles triangle; Base angles = 87°, vertex angle = 6°

The fourth isosceles triangle; Base angles = 86°, vertex angle = 8°

The vertices of the isosceles triangles form a arithmetic projection, with a common difference of 2°

Therefore, the vertex for next isosceles triangle = 8° + 2° = 10°

The base angles are derived from the sum of interior angles of a triangle which is 180°

Which gives;

2 × Base angles + Vertex angle = 180°

2 × Base angles + 10° = 180°

2 × Base angles = 180° - 10° = 170°

Base angles = 170°/2 = 85°

Base angles of the fifth isosceles triangle = 85°

From which we have;

The fifth isosceles triangle; Base angles = 85°, vertex angle = 10°

The measure of the vertex angle of the next (fifth) isosceles triangle = 10°

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P(x)=6x2+7x-5. g(x)=2x+3, if p(x)=g(x)q(X)+r(x), then find q(x) and r(x)

Answers

is the x in 6x2 referring to the variable or a multiplication sign?

Please help me with this im pretty confused ?

Answers

Answer:

a=6

Step-by-step explanation:

Since this is a right triangle, we can use the Pythagorean theorem

a^2 + b^2 = c^2 where a and b are the legs and c is the hypotenuse

a^2 + 8^2 = 10^2

a^2 + 64= 100

a^2 +64-64 = 100-64

a^2 = 36

Take the square root of each side

sqrt(a^2) = sqrt(36)

a = 6

Answer:

a = 6

The length of side a is 6.

Step-by-step explanation:

According to the question,

Using Pythagorean theorem

( a )² + ( b )² = ( c )²

Where, a and b are the base and c is the length of hypotenuse.

( a )² + ( 8 )² = ( 10 )²

evaluate the exponent

a ² + 64 = 100

subtract 64 from each side

a ² + 64 - 64 = 100 - 64

a ² = 36

Take the square root of each side

√a² = √36

a = 6

Solve using the Square-Root (x-3)²-49=0

Answers

Answer:

x equals 10 and x equals -4

Step-by-step explanation:

take the square root of (x-3)² and the square root of 49

√(x-3) = x-3

√49 = +7 and -7

substitute the positive and negative 7 in for 'x' and solve

x-3 = 7; therefore, x = 10

x-3 = -7; therefore, x = -4

Andrew is looking into prices for cable for his new home. He received the following breakdown for monthly prices.Basic Cable: $35.99
Cable boxes: $3.49 per cable box
HD Service: $9.99 per cable box
DVR: $14.99 per cable box
Installation Fee: $120.00 (one-time fee)

The total cost for 12 months of cable service with b cable boxes is represented by the expression below.
$551.88 + $341.64b

Which statement best describes the coefficient of "B"?

A. It is the cost for basic cable for one month and the installation fee.

B. It is the cost for basic cable for one year and the installation fee.

C. It is the cost for one cable box with DVR and HD service for one month.

D. It is the cost for one cable box with DVR and HD service for one year.

Answers

Given:

551.88 + 341.64b

The coefficient of "B" is 341.64, the best statement that applies to it is:

D. It is the cost for one cable box with DVR and HD service for one year.

Cable boxes: $ 3.49 per cable box
HD Service: $ 9.99 per cable box
DVR: $ 14.99 per cable box
Total : $ 28.47
multiply 12 months
Annual cost $341.64

Emma works in a department store selling clothing. She makes a guaranteed salary of $200 per week, but is paid a commision on top of her base salary equal to 25% of her total sales for the week. How much would Emma make in a week in which she made $2200 in sales? How much would Emma make in a week if she made x
x dollars in sales?