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2 years ago

Please help :(

Mathematics

1 answer:

densk [106]2 years ago

5 0

We have found the equations and angles for the given diagrams.

Since the angles are vertically opposite angles and they are equal, we get the equation as:

4 x - 5 = 2 x + 9

Solving for x:

4 x - 2 x = 9 + 5

2 x = 14

x = 7

2)Since the angles form a linear pair, their sum will be 180°.

The equation will be:

10 x + 4 + 3 x + 20 = 180°

Solving for x:

13 x + 24 = 180°

13 x = 156°

x = 12 °

Measure of ∠ACB = 10 x + 4

∠ACB = 10 (12) + 4 = 120 + 4

∠ACB = 124°

angle c is corresponding to angle g

angle e is alternate interior to angle c.

angle g is same side exterior to angle b.

Since ∠d = 40°,

∠b = 40° ( Vertically opposite angles.)

∠h = 40° ( corresponding angles)

∠e = 140° (co-interior angles).

Therefore, we have found the equations and angles for the given diagrams.

Learn more about angles here:

brainly.com/question/25716982

#SPJ9

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Read 2 more answers

Maths functions question

yarga [219]

Answer:

a) OA = 1 unit

b) OB = 3 units

c) AB = √10 units

Step-by-step explanation:

<u>Given function</u>:

$g(x)=2^x$

Point A is the y-intercept of the exponential curve (so when x = 0).

To find the y-value of Point A, substitute x = 0 into the function:

$\implies g(0)=2^0=1$

Therefore, A (0, 1) so OA = 1 unit.

If BC = 8 units then the y-value of Point C is 8.

The find the x-value of Point C, set the function to 8 and solve for x:

$\begin{aligned}f(x) & = 8 \\\implies 2^x & = 8\\2^x & = 2^3\\\implies x &= 3\end{aligned}$

Therefore, C (3, 8) so Point B is (3, 0). Therefore, OB = 3 units.

From parts (a) and (b):

A = (0, 1)
B = (3, 0)

To find the length of AB, use the distance between two points formula:

$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$\textsf{where }(x_1,y_1) \textsf{ and }(x_2,y_2)\:\textsf{are the two points.}$

Therefore:

$\implies \sf AB=\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}$

$\implies \sf AB=\sqrt{(3-0)^2+(0-1)^2}$

$\implies \sf AB=\sqrt{(3)^2+(-1)^2}$

$\implies \sf AB=\sqrt{9+1}$

$\implies \sf AB=\sqrt{10}\:\:units$

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