MATHEMATICS COLLEGE

Find all missing angles in the diagrams below, please help

Answers

Answer 1

Answer:

Answer:

x= 80°, y= 100°

Step-by-step explanation:

Please see the attached picture for the full solution.

Answer 2

Answer:

Answer:

x = 80,

y = 80

Step-by-step explanation:

This is difficult to explain, so here are the theorems used

two lines parallel, with a transversal; alternate interior angles,

verticle angles theorem,

parts - whole postulate,

verticle angles theorem,

parts- whole postulate,

sum angles in a triangle,

supplementary angle, definition straight angle,

parts- whole postulate,

there are many other ways to reach the answer, I just whent this way.

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Non examples of heterogeneous
The length of a rectangle is 16 meters and the width is 3 meters. Find the area.
Consider the following functions. f(x) = x − 3, g(x) = x2 Find (f + g)(x). Find the domain of (f + g)(x). (Enter your answer using interval notation.) Find (f − g)(x). Find the domain of (f − g)(x). (Enter your answer using interval notation.) Find (fg)(x). Find the domain of (fg)(x). (Enter your answer using interval notation.) Find f g (x). Find the domain of f g (x). (Enter your answer using interval notation.)
Find the numerical value of the log expression HELP PLS

A cinema seats 280 people. if 98 people are in the cinema, what percentage of the seats are filled ?

Answers

35 percent. Helps if you turn it into a fraction. so 98/280 is the same as .35 convert to percentage and you get 35%

The total number of seats are 280

Out of this 98 seats are filled

Hence it is expressed in fraction as $(98)/(280)$

(part out of whole)

To convert any fraction into percentage, we just need to multiply it with 100

$(98)/(280)$ ×100

$(9800)/(280)$

= 35 %

Hence 35% of the cinema is filled

The equation of a parabola is given.y=−14x2+4x−19

What are the coordinates of the vertex of the parabola?

Enter your answer in the boxes.

Answers

Answer:

vertex ( $(1)/(7)$ , $(131)/(7)$ ).

Step-by-step explanation:

Given : The equation of a parabola is given.

y=−14x²+4x−19

To find : What are the coordinates of the vertex of the parabola.

Solution : We have given that

y = −14x²+4x−19

we will be "completing the square" .

Factor out -14 to make leading coefficient 1

y = -14 ( $x^(2) -(2x)/(7) +(19)/(14)$ )

Add and subtract $((-1)/(7)) ^(2)$

y = -14 ( $x^(2) -(2x)/(7) +(19)/(14)+(-1)/(7)) ^(2) - ((-1)/(7))^(2))$ .

Complete the square

y = -14 ( $(x -(1)/(7)) ^(2) +(19)/(14)- ((-1)/(7))^(2))$ .

y = -14 ( $(x-(1)/(7)) ^(2) -(131)/(7)$

Standard form of parabola vertex form y = a(x - h)²+ k,

Where, ( h, k) are vertex

On comparing a = -14 , h= $(1)/(7)$ , k = $(131)/(7)$

Therefore, vertex ( $(1)/(7)$ , $(131)/(7)$ ).

The coordinates are 8, -3.

Find an equation of the sphere with center (-3, 2 , 5) and radius 4. What is the intersection of this sphere with the yz-plane.

Answers

Answer:

The equation of the sphere with center (-3, 2 , 5) and radius 4 is $(x+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$

The intersection of the sphere with the yz- plane gave the equation $(y-2)^(2) + (z-5)^(2) = 7$ which is a 2D- circle with center (0,2,5) and radius $√(7)$ .

Step-by-step explanation:

The equation of a sphere of radius r, with center (a,b,c) is given by

$(x-a)^(2) +(y-b)^(2) + (z-c)^(2) = r^(2)$

where, $x,$ $y,$ and $z$ are the coordinates of the points on the surface of the sphere.

Hence, the equation of the sphere with center, (-3, 2 , 5) and radius 4 becomes

$(x-a)^(2) +(y-b)^(2) + (z-c)^(2) = r^(2)$

$(x-(-3))^(2) +(y-(2))^(2) + (z-(5))^(2) = 4^(2)$

Then,

$(x+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$

This is the equation of the sphere with center (-3, 2 , 5) and radius 4,

Now, for the intersection of this sphere with the yz- plane,

The $yz -$ plane is where $x = 0$ , then we set $x = 0$

Them the equation $(x+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$ becomes

$(0+3)^(2) +(y-2)^(2) + (z-5)^(2) = 16$

$(3)^(2) +(y-2)^(2) + (z-5)^(2) = 16\n9 +(y-2)^(2) + (z-5)^(2) = 16\n(y-2)^(2) + (z-5)^(2) = 16 - 9\n(y-2)^(2) + (z-5)^(2) = 7$

This equation is the equation of a 2D- circle with center (0,2,5) and radius $√(7)$

This is the part of the sphere that intersects with the yz-plane.

What is the simplified form of this expression?

(5x2 + 2x + 11) − (7 + 4x − 2x2)

Answers

Answer:

7x² - 2x + 4

Step-by-step explanation:

(5x² + 2x + 11) - (7 + 4x - 2x²) = 5x² + 2x + 11 - 7 - 4x + 2x² =

(5x² + 2x²) + (2x - 4x) + (11 - 7) = 7x² - 2x + 4

Simplify.
28+3(5d-3)

Answers

Answer:

15d+19

Step-by-step explanation:

distribute 3(5d-3) first

= 15d-9

the expression is now 28+15d-9

combine 28 and -9

=19

bam u now have 15d+19

Identify the initial value, a, and base, b, of the function f(x)=ab^x if its graph passes through the points (0, 4) and (1, 20)

Answers

Answer:

a = 4, b = 5

Step-by-step explanation:

Given the exponential function

f(x) = a $b^(x)$

Use the given points to find a and b

Using (0, 4 ) , then

4 = a $b^(0)$ ( $b^(0)$ = 1 ) , thus

a = 4 , so

f(x) = 4 $b^(x)$

Using (1, 20 ) , then

20 = 4b ( divide both sides by 4 )

b = 5

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Find all missing angles in the diagrams below, please help​

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Find all missing angles in the diagrams below, please help