Mathematics High School

The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.
The four angles of the quadrilateral are °, °, °, and °, respectively.

Answers

Answer 1

Answer:

The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.

Step-by-step explanation:

Given  : The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.

To find : The four angles of the quadrilateral are °, °, °, and °, respectively.

Solution : We have given that  The four vertices of an inscribed quadrilateral divide a circle in the ratio 1 : 2 : 5 : 4.

Let the angle of the quadrilateral is x

Then all the  angles are  x  , 2x , 5x ,4x

Complete angle formed by circle is 360 °

Sum of all the angle are 360

x + 2x + 5x + 4x = 360 .

12 x = 360 .

On dividing both sids by 12.

x = 30 .

Then

2x =  60

5x = 5 * 30 = 150 .

4x = 4 *30 = 120 .

Therefore, The four angles of the quadrilateral are 30°, 60°, 150°, and 120°, respectively.

Answer 2

Answer:

for plato users the answers are 45,75,135,105

Step-by-step explanation:

Related Questions

The point (-2, 6) is on the line given by which of the equations below?





A.
y = 4x
 

B.
y = 2x
 

C.
y = 3x
 

D.
y = -3x

Answers

if we replace each equation with the proper set of values:
for (-2, 6) = (x, y) which also means that x = -2 and y = 6
A/ y = 4x => 6 = 4.(-2) <=> 6 = (-8)    Absurd
B/ y = 2.x => 6 = 2.(-2) <=> 6 = (-4)   Absurd
C/ y = 3x => 6 = 3.(-2) <=> 6 = (-6)    Absurd
D/ y = -3x => 6 = (-3).(-2) <=> 6 = 6   Right Answer

A parabola has a focus of F(2, -0.5) and a directrix of y=-1.5 P(x,y) represents any point on the parabola, while D(x, -1.5) represents any point on the directrix.

What are the steps required to find the equation of the parabola?

Answers

The sketch of the parabola is attached below

We have the focus [tex](a,b) = (2, -0.5)[/tex]
The point [tex]P(x,y)[/tex]
The directrix, c at [tex]y=-1.5[/tex]

The steps to find the equation of the parabola are as follows

Step 1
Find the distance between the focus and the point P using Pythagoras. We have two coordinates; [tex](2, -0.5)[/tex] and [tex](x,y)[/tex].
We need the vertical and horizontal distances to find the hypotenuse (the diagram is shown in the second diagram).
The distance between the focus and point P is given by
[tex] \sqrt{ (x-a)^{2}+ (y-b)^{2} } [/tex]

Step 2
Find the distance between the point P to the directrix [tex]c[/tex]. It is a vertical distance between y and c, expressed as [tex]y-c[/tex]

Step 3
The equation of parabola is then given as 
[tex] \sqrt{ (x-a)^{2}+ (y-b)^{2} } [/tex]=[tex]y-c[/tex]
[tex] (x-a)^{2}+ (y-b)^{2}= (y-c)^{2} [/tex] ⇒ substituting a, b and c
[tex] (x-2)^{2}+ (y--0.5)^{2} = (y--1.5)^{2} [/tex]
[tex] (x-2)^{2}+ (y+0.5)^{2}= (y+1.5)^{2} [/tex]⇒Rearranging and making [tex]y[/tex] the subject gives

[tex]y= \frac{ x^{2} }{2} -2x+1[/tex]

A point on an ellipse is 11 units from one focus and 7 units from the other. What is the length of the major axis?

Answers

A diagram of an ellipse is shown below

VW is the major axis
ST is the minor axis
P is a point on the ellipse
A and B are the foci (or focus)

The length of major axis is given by either VA+AW or AP+BP
One useful fact to know that AP+BP is constant wherever the point P is on the ellipse

We know that the distance of the point 'P' from one focus is 11 units and from the other focus is 7 units, so we know the length of AP and BP.

Hence, the length of major axis is 11+7=18 units

The length of a rectangle is eight times it's width. If the length was decreased by 10 meters and the width decreased by 2 meters the area would be decreased by 162 m. Find the original dimensions.

Answers

Alright, so l=8w (l=length, w=width, a=l*w or original area)

(l-10)*(w-20)=a-162

Substituting l for 8w and a for l*w and then 8w*w, we have
 (8w-10)(w-20)=8w^2-162=8w^2-160w-10w+200=8w^2-170w+200

8w^2-170w+200=8w^2-162 , so we subtract 8w^2 from both sides as well as subtract 200 to both to get -170w=-362, so w=362/170 and
 l= 8*362/170=2896/170 

Where do the following graphs intersect? Show how you can find the intersection point algebraically.

1) y-2x=3
2) y-3= x^2

Answers

Solve equation (1) for y
y-2x = 3
y-2x+2x = 3+2x
y = 2x+3

Plug that into equation (2)
y - 3 = x^2
2x+3 - 3 = x^2
2x = x^2

Get everything to one side
2x = x^2
2x-2x = x^2-2x
0 = x^2-2x
x^2-2x = 0

Now factor and use the zero product property to find the solutions for x
x^2-2x = 0
x(x-2) = 0
x = 0 or x-2 = 0
x = 0 or x = 2

If x = 0, then y is...
y = 2x+3
y = 2(0)+3
y = 3
So (x,y) = (0,3) is one solution of the system. This is one point where the graphs intersect.

If x = 2, then y is...
y = 2x+3
y = 2(2)+3
y = 4+3
y = 7
So (x,y) = (2,7) is another solution to the system. This is another point where the graphs intersect.

See the attached image for a visual. The two curves cross at point A and point B
A = (0,3)
B = (2,7)

(06.06) Which of the following demonstrates the Commutative Property of Multiplication? 3(4a − 2) = 12a − 6 3(4a − 2) = (4a − 2) ⋅ 3 12a − 6 = (4a − 2) ⋅ 3 (3 ⋅ 4a) − 2 = 3(4a − 2)

Answers

commutative property of multiplication states : a * b = b * a...so basically, u can move the numbers around and it will still equal the same thing
3(4a - 2) = (4a - 2) * 3 <==
Commutative means you can reverse the order  without affecting the result of the multiplication:-   a*b = b*a.
so its the second option:-

3(4a - 2) = (4a - 2).3

Use the given graph to determine the limit, if it exists.
limf(x)
x-->2

Answers

Answer:

Step-by-step explanation:

4

The limit as x tends to 2 is -1

How to find the limit

The limit is sought by investigating the graph. More attention is directed to when the domain or the x-value is at 2.

It can be observed that at this point we have 2 open dots and one closed dot.

The closed dot implies there is a value for x = 2, hence we trace the y coordinate at this point.

Tracing the y coordinate shows that the value is -1

Select the additive inverse of 51

Answers

-51 because it makes zero
The additive inverse of a number is a number when added to the original number equals to 0.

What can we add to 51 to make it equal to 0. Set up an equation.

Let x = the additive inverse of 51

x + 51 = 0

Solve for x.

x + 51 = 0
x = -51 <-- Subtract 51 from both sides

So, -51 is the additive inverse of 51.

What is 
5.63×
10
−6
in decimal form?

a. 0.00000563

b. 0.000000563

c.5,630,000

d. 56,300,000

Answers

your answer would be A.

The sum of two real numbers is 18 and the product is 70. what are the two numbers?

Answers

let the numbers be x and y:
x+y=18......i
xy=70.........ii
from i
y=18-x.....iii
from ii
y=70/x......iv
substituting iii in iv we get:
70/x=18-x
multiplying through by x;
70=18x-x^2
x^2-18x+70=0
x=12.3 or 5.7
thus:
x=12.3 and y=5.7





The sum of six consecutive odd numbers is 204. What is the fourth number in the sequence

Answers

x+x+2+x+4+x+6+x+8+x+10 = 204
6x + 30 = 204
6x = 174
x = 29
six consecutive odd numbers are 29,31,33,35,37,39

answer
the fourth number in the sequence is 35


let numbers be

2n+1 , 2n+3, 2n+5, 2n+7, 2n+9,2n+ 11  and these add up to 204

12n + 36 = 204
12n = 168
n = 14

so fourth number in the sequence is 2(28) + 7 = 63

if a metal tool chest has the shape of a prism with a pentagonal base of 6194in squared in area, calculate the volume of the metal chest and pick where length c = 6 inches and length m = 19 inches

Answers

The formula for the volume of most prism is area of base(height) so just multiply 43in(21in) to get answer

The volume of the metal tool chest is 37,164 cubic inches. To calculate the volume of the metal tool chest, we use the formula for the volume of a prism: Volume = Base area × Height

Given that the pentagonal base has an area of 6194 square inches, and the length c (which represents the height) is 6 inches, we can calculate the volume as follows:

Volume = 6194 in² × 6 in

Volume = 37,164 cubic inches

So, the volume of the metal tool chest is 37,164 cubic inches.

As for the lengths provided:

c = 6 inches (height)

m = 19 inches (unknown side length of the pentagon)

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How you know when there is only one solution triangle possible from a side-side-angle?

Answers

Answer:

There will be only on solution if either of these conditions is met:

the given angle is opposite the longest sidethe triangle is a right triangle (the ratio of the side opposite the angle to the other given side is equal to the sine of the angle)

Step-by-step explanation:

Consider the SSA geometry with the angle placed in standard position at the origin and its adjacent given side (the second side of SSA) extending along the +x axis. Draw a circle having a radius equal to the length of the first side of SSA, centered on the vertex between the two segments on the +x axis.

There are three possibilities for the way this circle intersects the other ray of the angle (the ray that is not the x-axis):

the first side is as long or longer than the second side, so there is one point of intersection (one solution to the triangle, purple in the attachment)the first side is just long enough to be tangent to the other ray, so there is one point of intersection (one solution to the triangle, green in the attachment)the first side is between these lengths, so intersects the other ray in two places, giving two solutions to the triangle, red in the attachment.

The parabola has a vertex of (1,-16) and y intercept of (0,-15) that crosses the x axis in two places. one x intercept is (5,0) what is the other x intercept

Answers

vertex form is:

y = a(x - 1)^2 - 16  where a is a cosntant

at y intercept we have

-15 = a^2 - 16
a^2 = 1

so equation of the parabola is y = (x-1)^2 - 16

the equation of symmetry is x = 1  and both roots are same distance either side of the point (1,0) so the other x-intercept  is  1 - 4 =   (-3,0)   

The area of a rectangular wall of a barn is 75 75 square feet. its length is 10 10 feet longer than the width. find the length and width of the wall of the barn.

Answers

A = L * W
A = 75
L = W + 10

75 = W(W + 10)
75 = W^2 + 10W
W^2 + 10W - 75 = 0
(W + 15)(W - 5) = 0

W + 15 = 0
W = -15...not this one because it is negative

W - 5 = 0
W = 5 <=== width is 5 ft

L = W + 10
L = 5 + 10
L = 15 <=== length is 15 ft
Final answer:

First, represent the unknown width as 'x'. Then, because the length is 10 feet more than the width, represent the length as 'x + 10'. Since the area is 75 square feet, set up and solve the equation x*(x + 10) = 75 for 'x'. This will give the width and the length will be this width plus 10 feet.

Explanation:

This problem can be solved using algebra. First, let's denote the width of the wall as x in feet. If the length of the wall is 10 feet longer than the width, then we can express the length as x + 10. We're told that the area of the rectangle formed by the wall is 75 square feet. The area of a rectangle is calculated by multiplying its length by its width. Therefore:

x*(x + 10) = 75

You can solve this quadratic equation for x. The positive solution will be the width of the wall and the length will be that value plus 10 feet.

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Find the circumference of a circle with radius of 18 in. Leave your answer in terms of π

Answers

C=2πr
C=2(18)π
C=36π in.
The formula for circumference is 2*pi*r

C = 2*pi*18
C = 36pi

a bag contains 5 red marbles, 3 yellow marbles, and 2 blue marbles. Once a marble is drawn, it is not replaced.what is the probability of drawing a blue on the first draw and a second blue marble on the next draw ?

Answers

5 red, 3 yellow, and 2 blue....for a total of 10 marbles

P(first one being blue) = 2/10 which reduces to 1/5
not replaced
P(second one is blue) = 1/9...because u already pick a blue, meaning there is only 1 left, and there is one less marble, so there is a total of 9 marbles.

P(both events happening) = 1/5 * 1/9 = 1/45 <==

The distance from earth to the moon is about 22^4 miles. the distance from earth to neptune is22^7 miles. which distance is the greatest and by how much

Answers

22^4=22x22x22x22
22^7=22x22x22x22x22x22x22
This means that 22^7 is greater and by the amount of 22^3

PQRS is an isosceles trapezoid and m angle Q=127. Find M angle P.

Answers

PQRS is an isosceles trapezoid and m < Q=127

so m<Q = m<P =127



answer
127

Answer:

[tex]m<P=127\°[/tex]

Step-by-step explanation:

we know that

If the trapezoid PQRS is an isosceles trapezoid

then

[tex]PS=QR[/tex] ----> congruent sides

[tex]m<P=m<Q[/tex] -----> congruent angles

In this problem we have

[tex]m<Q=127\°[/tex]

therefore

[tex]m<P=127\°[/tex]

1. In how many different ways can 5 people be seated at a round table?


2. Each block on the grid is 1 unit by 1 unit. We wish to walk from A to B via 7 unit path but we have to stay on the grid. How many different paths can we take?

3. How many different "words" can be made from the given word by re-arranging the letters?

a) VECTOR

B) TRUST

Answers

1. 

Assume the people A, B, C, D and E are sitting in a row.

since there are 5 positions, they can sit in 5*4*3*2*1=120 ways.

consider 1 certain sitting position, for example ABCDE, that is B has A to his right, C to his left. D has C to his right and E to his left. And so on.

the positions 

ABCDE
BCDEA
CDEAB
DEABC
EABCD

while in a row are different positions, in a round table they are the same thing.

(read the letters starting from A, and when the letters finish, continue reading from the beginning of the row. They all read "ABCDE")

This means that any arrangement in a round table, is converted to 5 arrangements in a row.

So there are in total  [tex] \frac{5!}{5}=4*3*2*1=24 [/tex] arrangements of 5 people around a table.

2. check picture.

Consider the case where A is at (2, 2) and B is at (5, 6)

A can move to B through 3 horizontal units to the right, we call them E (for East) and 4 vertical units up, which we call N (for north).

the total path is 7 units.

it can be done in several ways, for example:

ENNNENE (the red path shown in the figure)
NNEEENN (the black path shown in the figure)

In total there are 
[tex] \frac{7!}{3!*4!}= \frac{7*6*5*4!}{3!*4!}= \frac{7*6*5}{3!}= 35 [/tex] paths.

Remark: 7! is the number of arrangements if the letters were different. We divide by 3! because of the 3 E's and 4! because of the 4 N's. 

Another possibility could be A'(3, -5), B'(8,-3).

From A' to B' we go by a total of 5 E and 2 N, so there are 

[tex] \frac{7!}{2!*5!}= \frac{7*6*5!}{2!*5!}= \frac{7*6}{2}= 42 [/tex] paths in total.
there is one more possibility
[tex] \frac{7!}{1!(6!)}=7 [/tex]

C.

a) consider the letters {V,E,C,T,O,R}

we can form 6*5*4*3*2*1=720 words, as the first digit can be any of the 6 letters, combined with 5 for the second letter and so on.

b) the difference with a is that we have 5 letters and we have 2 T.

we have in total 5*4*3*2*1=120 arrangements of these letters, if the 2 T's were considered as separate.

consider the arrangements:

[tex]T_1RUST_2[/tex] and [tex]T_2RUST_1[/tex].

We read bth as just TRUST, but the permutation formula 5*4*3*2*1 considers these as 2 different.

this is why we need to divide 120 by 2, to get the actual number of words that can be formed. So the number is 60.

Answers:

1) 24

2) 7, 35 or 42. it depends on the positions of A and B, check the solution

3) a-720, b-160
 

find the value of x if f(x) equals 7 f(x) equals 4x minus 1

Answers

The answer for this question is x=2

Don is 6 feet tall. at a given time of day, he measures his shadow to be 13 feet long. at the same time, he measures the shadow length of a nearby tree to be 51 feet. how tall is the tree

Answers

Don is 6 feet tall. at a given time of day, he measures his shadow to be 13 feet long. at the same time, he measures the shadow length of a nearby tree to be 51 feet. how tall is the tree(x=tree height)

the equation for this problem would be...
6/13=x/51
you then multpli the denominators on both sides and get...
6*51=13x
you then solve...
306=13x
and then you divide 13 on both sides...
x=23.54ft
the tree is 23.54ft tall

(leave a thanks and a rating if i helped) c:

The height of the tree maintaining the given ratio is 23.54 feet.

What are the ratio and proportion?

The ratio is the division of the two numbers.

For example, a/b, where a will be the numerator and b will be the denominator.

Proportion is the relation of a variable with another. It could be direct or inverse.

Given that,

Don height = 6 feet

His shadow = 13 feet

The ratio of height to shadow = 6/13

Tree height = x (let's say)

Tree shadow = 51 feet

Ratio = x/51

Both ratios must be the same, therefore,

x/51=6/13

x=23.54 feet

Hence "The height of the tree maintaining the given ratio is 23.54 feet".

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What is 5.928301 to 2 decimal places?

Answers

Final answer:

To round 5.928301 to 2 decimal places, we observe the third decimal place. It's 8, so we round up, making the answer 5.93.

Explanation:

When rounding the number 5.928301 to 2 decimal places, we need to look at the third decimal digit to decide whether to round up or down. Since the third decimal digit (8) is greater than 5, we round up. Therefore, the number 5.928301 rounded to 2 decimal places is 5.93.

Rounding a number to two decimal places involves examining the third decimal digit to determine whether to round up or down. In the case of 5.928301, the third digit is 8, which is greater than 5. Consequently, rounding up is necessary. Thus, the rounded value of 5.928301 to two decimal places is 5.93, emphasizing the role of the third digit in the rounding decision.

the leg of a right triangle is 5 units and the hypotenuse is 8 units.what is the length in units of the other leg of the triangle

Answers

Using the Pythagorean Theorem, we can figure out the missing leg.

If you don't know, the Pythagorean Theorem states that for any right triangle the sum of the squares of both of the legs is equals to the hypotenuse.

[tex]a^2 + b^2 = c^2[/tex]

Where the variables a and b are the legs and c is the hypotenuse.

The variables a and b are interchangeable but not c.

Plug in the values that we know.

[tex]5^2 + b^2 = 8^2[/tex]
[tex]25 + b^2 = 64[/tex]
[tex]b^2 = 39[/tex]
[tex]b = \sqrt{39}[/tex]

So, the other leg is equal to the square root of 39 units.

The square of the hypotenuse is equal to the sum of the square of other two sides. The length in units of the other leg of the triangle is 6.2 units

What is Pythagoras theorem?

The square of the hypotenuse is equal to the sum of the square of the other two sides.

Mathematically;

l^2 = a^2 + b^2

Given

l = 8 units

a = 5 units

Substitute

8^2 = 5^2 + b^2

64 - 25 = b^2

b^2 = 6.2units

Hence the length in units of the other leg of the triangle is 6.2 units

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Sue took a taxi from her home to her friends house. It cost $3.58 per mile and she gave the driver a $5 tip. If she paid $87.34, how many miles does she live from her friend?

Answers

87.34-5 = 82.34

82.34/3.58 = 23

 she lives 23 miles away

Find the value of x for which abcd must be a parallelogram 5x-1 2x+5

Answers

If ABCD is a parallelogram then:
5 x - 1 = 2 x + 5
5 x - 1 + 1 = 2 x + 5 + 1
5 x - 2 x = 2 x - 2 x + 6
3 x = 6
x = 6 : 3
Answer:
x = 2

Which of the following sets is not finite?

Answers

pricherter plese.............
In which sphere would lightning be found?

The range of a projectile fired at an angle θ with the horizontal and with an initial velocity of v 0 feet per second is r = 1 v 20 sin 2θ where r is measured in feet. a golfer strikes a golf ball at 120 feet per second. 32 ignoring the effects of air resistance, at what angle must the golfer hit the ball so that it travels 140 feet? (round answer to nearest angle.)

Answers

Projectile motion is characterized by a motion that has two vector forces: the velocity along the x and y directions. As a result, the motion follows an arc-shaped direction. These two directions are actually independent of each other. 

There are already derived equations for this so it is already convenient. However, your given equation for range is incomplete. The correct equation is:

R = v₀²sin2θ/g

where
R = 140 ft
v₀ = 120 ft/s
g = 32.2 m/s²

Substituting the values,

sin 2θ = Rg/v₀²
sin 2θ = (140)(32.2)/(120²)
sin 2θ = 0.313
2θ = sin ⁻¹ (0.313)
2θ = 18.24°
θ =18.24°/2
θ = 9.12°

if M and N are midpoints in a diagram below, determine values for x and y

Answers

Research scientists use a standard practice called the _____ method to help them understand phenomena.
In a triangle the midline joining the midpoints of two sides is parallel to the third side and half as long ⇒
AС = 2*MN
3x + 10 = 2(x+5)
3x + 10 = 2x + 10
3x - 2x = 10 - 10
x = 0

M is a midpoint of AB ⇒
AM = BM
3y - 8 = 2(y+1)
3y - 8 = 2y + 2
3y - 2y = 2 + 8
y = 10

What polynomial identity should be used to prove that 20 = 36 − 16

Answers

Difference of Squares :)

Diffrence of squares is the correct answer just score pract q


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