MATHEMATICS HIGH SCHOOL

How do you answer these questions?

Answers

Answer 1

Answer:

First page:

Angles B and C >>> vertical angles

C + D is 180 because they form a >>> straight line

D and E are congruent bc they are alternating interior.

Second page:

If A = 72 degrees, then D is 72 degrees. E and G would also be 72 degrees.

If A = 72, just remember that A + B = 180 (bc together they are a straight line), so 180-72 = 108. So Angle B is 108 degrees.

If B is 108 degrees, then C, F and H are also 108 degrees.

So the actual questions in the order listed:

B = 108 degrees

D = 72 degrees

E = 72 degrees

F = 108 degrees

H = 108 degrees

G = 72 degrees

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find the first,fourth,and tenth terms of the arithmetic sequence described by the given rule. A(n)=5+(n-1)(1/6)

Answers

Answer:

First term is 5

Fourth term is 5.5

Tenth term is 6.5

Step-by-step explanation:

Given :The rule as $A(n)=5+(n-1)((1)/(6))$

We have to find find the first,fourth,and tenth terms of the arithmetic sequence.

Consider the given rule ,

$A(n)=5+(n-1)((1)/(6))$

For first term , put n = 1

$A(1)=5+(1-1)((1)/(6))$

Simplify , we have,

$A(1)=5$

For fourth term, Put n = 4

we have,

$A(4)=5+(4-1)((1)/(6))$

Simplify, we have,

$A(4)=5+(3)((1)/(6))$

$A(4)=5+(1)/(2)=5.5$

For tenth term, put n = 10 ,

We have,

$A(10)=5+(10-1)((1)/(6))$

$A(10)=5+(9)((1)/(6))$

$A(4)=5+(3)/(2)=6.5$

Thus, First term is 5

Fourth term is 5.5

Tenth term is 6.5

a₁ = 5 an = a₁ + ( n-1) * r
wyliczymy jednak - so we enumerate
a₁ = 5 + (1-1) * (1/6) = 5 + 0* 1/6 = 5 + 0 = 5
a₄ = 5 + (4 - 1) * (1/6) = 5 + 3 * (1/6) = 5 + 3/6 =5 1/2 = 5,5
a₁₀ = 5 + (10 - 1) * (1/6) = 5 + 9 * (1/6) = 5 + (9/6) = 5 + 3/2 = 6 1/2 = 6,5

Triangle UVW is drawn with vertices at U(−1, 1), V(0, −4), W(−4, −1). Determine the coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 90° counterclockwise

Answers

The coordinates of the vertices for the image, triangle U′V′W′, if the preimage is rotated 90° counterclockwise include the following:

U' = (1, 1).

V' = (-4, 0).

W' = (-1, 4).

What is a rotation?

In Mathematics and Geometry, the rotation of a point 90° about the center (origin) in a counterclockwise (anticlockwise) direction would produce a point that has these coordinates (-y, x).

By applying a rotation of 90° counterclockwise to the vertices of triangle UVW, the coordinates of the vertices of the image are as follows:

(x, y) → (-y, x)

Ordered pair U = (-1, 1) → Ordered pair U' = (1, -(-1)) = (1, 1).

Ordered pair V = (0, -4) → Ordered pair V' = (-4, -(0)) = (-4, 0).

Ordered pair W = (-4, -1) → Ordered pair W' = (-1, -(-4)) = (-1, 4).

Read more on rotation here: brainly.com/question/28854313

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Simplify the rational expression. State any restrictions on the variablen^4-10n^2+24/ n^4-9n^2+18

Answers

Answer:

The simplified form is $=((n-2)(n+2))/((n-\sqrt3)(n+\sqrt3))$

The variable n can not be equals to $\pm\sqrt3$ as for these value denominator equals to zero which becomes an indeterminate form.

Step-by-step explanation:

we have to simplify the rational expression and state the restrictions on the variable.

$(n^4-10n^2+24)/(n^4-9n^2+18)$

We can now see that both the numerator and denominator are quadratic trinomials in $n^2.\$

We split the middle terms as follows;

$(n^4-10n^2+24)/(n^4-9n^2+18)=(n^4-6n^2-4n^2+24)/(n^4-3n^2-6n^2+18)$

$=(n^2(n^2-6)-4(n^2-6))/(n^2(n^2-3)-6(n^2-3))$

$=((n^2-4)(n^2-6))/((n^2-6)(n^2-3))$

$=((n-2)(n+2))/((n-\sqrt3)(n+\sqrt3))$

which is the simplified form of given expression.

The variable n can not be equals to $\pm\sqrt3$ as for these value denominator equals to zero which becomes an indeterminate form.

The answer to the question is n^2-4/n^2-3 n ≠±√6±√3

Math help pleaseeeeee