What is the ratio of the side length of the side opposite any 30 degree angle and the length of the hypothesis ?

Answers

Answer 1

Answer:

1 : 2

Step-by-step explanation:

the ratio is 1 : 2

_____


Related Questions

Find two consecutive positive intergers such that the square of the smaller interger is nineteen more than five times the larger interger.

Answers

Answer:

8 and 9

Step-by-step explanation:

Let the two consecutive integers be x - 1 and x

Smaller = x-1

Largere = x

If the square of the smaller integer is nineteen more than five times the larger integer, then;

(x-1)² = 19 + 5x

Expand

x²-2x+1= 19+5x

x²-2x-5x+1-19 -0

x²-7x-18 =0

Factorize

x²-9x+2x-18 =0

x(x-9)+2(x-9) = 0

(x+2) = 0 and x - 9 = 0

x = -2 and 9

SInce x cannot be negative;

x = 9

Smaller number = 9-1

Smaller number = 8

Hence the two consecutive integers are 8 and 9

Find all values of x that satisfy the equation below. (x + 1)² - 25/9
= 0​

Answers

Answer:

x = 8/3, 2/3

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Multiple Roots

Step-by-step explanation:

Step 1: Define

Identify

(x + 1)² - 25/9 = 0

Step 2: Solve for x

[Addition Property of Equality] Add 25/9 on both sides:                               (x + 1)² = 25/9[Equality Property] Square root both sides:                                                    x + 1 = ±5/3[Subtraction Property] Subtract 1 on both sides:                                            x = ±5/3 - 1Evaluate Addition/Subtraction:                                                                        x = 8/3, 2/3

Step-by-step explanation:

Hey there!

Given equation is:

(x+1)² - 25/9 = 0

Then;

(x+1)² - (5/3)² = 0 ( since 5² = 25 and 3² = 9)

or, {(x+1)+5/3} { (x+1)-5/3} = 0. { use a² - b² = (a+b)(a-b) formula}

[tex]( \frac{3x + 3 + 5}{3} )( \frac{3x + 3 - 5}{3} ) = 0[/tex]

[tex]( \frac{3x + 8}{3} )( \frac{3x - 2}{3}) = 0[/tex]

Now;

Either;

( \frac{3x + 8}{3}= 0

or, X = 8/3

Or,

( \frac{3x -2}{3} = 0

x = 2/3

Therefore, X = 8/3 or 2/3.

Hope it helps!

Use the data in the table to complete the sentence. x y –2 7 –1 6 0 5 1 4 The function has an average rate of change of __________.

Answers

Answer:  To find the average rate of change, evaluate the function at the given points.

Evaluate the difference of the function at the given points.

Divide the difference of the function at the given points with the difference of the given points.

Step-by-step explanation:

The Average of rate is -1.

Everytime it goes up by one the y goes down by 1 so it would be -1.

The average rate of change of the function in the table given is: -1.

What is Average Rate of Chnge of a Function?

Average rate of change of a function = change in y / change in x = rise/run.

Given the table representing a function, and using two set of ordered pairs, (-2, 7) and (0, 5):

Average rate of change of the function = (7 - 5)/(-2 - 0)

Average rate of change of the function = 2/-2

Average rate of change of the function = -1.

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Please please help me

Answers

Answer:

may be the answer is 1000.not sure.

Answer:

answer is c 1600

hope it helps

what two numbers add up to 55 and multiply to -375​

Answers

Answer:

-6.13406 and 61.13406

Step-by-step explanation:

x + y = 55

x × y = -375

y = 55 - x

x × (55 - x) = -375

55x -x² = -375

x² - 55x - 375 = 0

solution of a quadratic equation :

x = (-b ± sqrt(b² - 4ac))/(2a)

a=1

b=-55

c=-375

x = (55 ± sqrt(55² + 4×375))/2 = (55 ± sqrt(4525))/2 =

= (55 ± sqrt(25 × 181))/2 = (5×11 ± 5×sqrt(181))/2 =

= 5/2 × (11 ± sqrt(181)) =

= 61.13406... or -6.13406...

y = 55 - 5/2×(11 ± sqrt(181)) = 55/2 ± 5/2×sqrt(181) =

= -6.13406... or 61.13406...

61/2×(8/9÷13/18)+(3/4) of 31/5​

Answers

Answer:

[tex]\frac{10969}{260}[/tex]

Step-by-step explanation:

please answer this 2 question​

Answers

Answer:

Step-by-step explanation:

AP 1 : 12, 15 , 18 , 21, 24, 27, 30 , 33 , 36, 39,.....

AP 2 : 17 , 21 , 25 , 29, 33, 37 , 41, 45,.....

AP formed with the common terms:  21, 33, 45 , ......

a = 21 , d = 33-21 = 12 ; n = 100

Sum = [tex]\frac{n}{2}(2a +(n-1)d)[/tex]

       [tex]=\frac{100}{2}[2*21+99*12]\\\\=50 * [42+1188]\\\\=50*1230\\\\= 61500[/tex]

A general formula for a parabola is y2=4px.

What is the value of p in the equation y2=−4x?



P=−4
P=−1
P=1
P=4

Answers

Answer:

P = -1

Step-by-step explanation:

-1 x 4 = -4

The solution is : p= -1, is the value of p in the equation y^2=−4x.

What is equation?

An equation is a  mathematical statement that is made up of two expressions connected by an equal sign.  In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal.

here, we have,

Explanation:

We have been given parabola along positive side of x-axis with equation

y² = 4px

and, y² = -4x

after equating the values of  y² we will get

4px =-4x

Divide each term by x on both left hand side and right hand side  we will get

4p= -4

Now, divide each term by 4 on both left hand side and right hand side we will get the final result p=-1

Hence, The solution is : p= -1, is the value of p in the equation y^2=−4x.

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Which relationship has a zero slope?

Answers

Answer:

b has zero slop mark me as a brilliant

B has zero slope mark

20 marbles in a bag. 4 are red, 5 are blue, 5 are black, 4 are white and 2 are yellow. What is the probability that he pulls out a red marble?

Answers

Answer:

1/5

Step-by-step explanation:

Probability calculates the likelihood of an event occurring. The likelihood of the event occurring lies between 0 and 1. It is zero if the event does not occur and 1 if the event occurs.

For example, the probability that it would rain on Friday is between o and 1. If it rains, a value of one is attached to the event. If it doesn't a value of zero is attached to the event.

probability that he pulls out a red marble = number of red marbles / total number of marbles

= 4/20 = 1/5

Which best describes the relationship between the line that passes through the points (-6, -1) and (-11, 1) and the line
that passes through the points (-3, -8) and (-5, -13)?
A. perpendicular
B. parallel
C. neither perpendicular nor parallel
D. same line

Answers

Answer: A. perpendicular

Step-by-step explanation: First, you have to determine the slope of both lines and you can do so using the slope formula: (y2 - y1)/(x2 - x1). You should get the slope -2/5 for the first line and 5/2 for the second. Because one line has a slope that is the negative reciprocal of the other, these lines are perpendicular.

Find C. See the image below

Answers

Answer:

55 degrees

Step-by-step explanation:

First, we can use Thales' Theorem to determine that because AC is along the circle's diameter, angle B (the angle opposite to that side) is a right angle.

Next, we know that an inscribed angle with its vertex on the circle, formed by two intersecting chords (A in this case) is equal to 1/2 of its intercepted arc, so angle A = 70/2=35

We can then use the fact that a triangle adds up to 180 degrees here to get

35+90+C=180

C=55 degrees

Two large parallel metal plates carry opposite charges. They are separated by 85mm. The work done by the field is 6x10-3J and its field exerts on a particle with charge +8µC. Calculate the surface charge density on each plate.

Answers

Answer:

The surface charge density is [tex]7.8\times10^{-8} C/m^2[/tex].

Step-by-step explanation:

separation, d = 85 mm

Work, W = 6 x 10^-3 J

charge , Q = 8µC

The potential difference is given by

W = q V

[tex]V=\frac{6\times 10^{-3}}{8\times 10^{-6}}=750 V[/tex]

Let the charge on he capacitor is q.

[tex]q = CV\\\\q = \frac{\varepsilon oA}{d}\times V\\\\\frac{q}{A} = \frac{8.85\times 10^{-12}\times750}{0.085} =7.8\times10^{-8} C/m^2[/tex]

A piece of ribbon is cut into two pieces in the ratio 3:7. The length of the shorter piece is 45cm. Calculate the length in cm of the longer piece of ribbon.​

Answers

Answer:

105 cm

Step-by-step explanation:

3/7 = 45/x

cross-multiply:

3x = 315

x = 105

I NEED HELP PLZ it is very much appreciated

Answers

Answer:

C

Step-by-step explanation:

average, average, average

if there is one dot to the right that is far away and 3 dots to the left that are close to the like, estimated distance of the right dot would be 3 and the total distance sum of each dot to the left is 3, so the line would be between the 1 right dot and 3 left dots

Answer:

D

Step-by-step explanation:

D has three dots near to the line

hey !! solve it

[tex] \sqrt{44 \times 11} [/tex]

Answers

Step-by-step explanation:

✓44×11

=✓2²×11²

=22

!!!!????!!!!!!

Answer:

22

Step-by-step explanation:

First, multiply 11 and 44

11 × 44 = 484

[tex]\sqrt{484}[/tex] = 22

---------------------------------------------------------------------------------------------------------------

Have a great summer :)

In a regular polygon each interior angle is 120 greater than each exterior angle. Calculate the number of sides of the polygon.

Answers

Answer:

12 sides.

Step-by-step explanation:

the sum of every pair of interior and exterior angle is always 180 degrees.

x = exterior angle.

the interior angle is then x+120.

so then exterior and interior angle together must be 180.

x + x + 120 = 180

2x + 120 = 180

2x = 60

x = 30 degrees

how many sides ?

the sum of all exterior angles must be 360 degrees.

all exterior angles are the same (because all the interior angles must be the same due to "regular polygon").

so, how many times does 30 fit into 360 ?

360/30 = 36/3 = 12

it has 12 corners and also sides.

There is a bag with only red marbles and blue marbles. The probability of randomly choosing a red marble is 1 /9 . There are 63 marbles in total in the bag and each is equally likely to be chosen. Work out how many red marbles there must be.

Answers

Answer: 7 red marbles.

Step-by-step explanation:

Since we are given the information that there are only red marbles and blue marbles in the bag and that the probability of randomly choosing a red marble is 1 /9 while there are 63 marbles in total.

Then the number of red marbles will be:

= 1/9 × 63

= 7

There are 7 red marbles

The number if blue marbles will be:

= 63 - 7

= 56 blue marbles

Write the equation of the line that contains the points (-2,5) and (6,9).

Answers

Answer: y=2/4x+6

I think it´s right sorry if it is´nt

a fruit seller had thought to sell 120kg of fruit at 150 dollars / kg but sold it 5% less. find out how much dollars the seller lost​

Answers

900$ loss

X/150=.05/1
x= 142.5

120(142.5)=17100
120(150)= 18000

18000-17100= 900

Help please!
Brainliest + 20 points

Answers

Answer:

im not sure but pls gimme brainlyist bc im a dum dum

Step-by-step explanation:

I am not really sure either looks hard

А
3
-2
-1
0
2
3
B.
-1
The distance AB rounded to the
nearest tenth = [?]
Hint: d= (x2 - 1)+ (y2 - yı)2

Answers

The answe is 4.5
Here is The work shown below:

APB is parallel to CTRD. PQRT is a quadrilateral. work out the size of the angle marked x you must show your working

Answers

Answer: X would be 84 degrees.

Step-by-step explanation: APB is a straight angle, which adds up to 180 degrees. TPQ is  90 degrees, and QPB is 32 degrees, so 180-90-32=58. APT is 58 degrees. APT and PTR are alternate interior angles, therefore they have the same angle measure. So PTR is also 58 degrees. A quadrilateral adds up to 360 degrees, so add up the three known angles in the quadrilateral, 58+90+128, which gives you 276 degrees. 360-276=84 degrees, therefore X would be 84 degrees.

If there are twice as many bicycles as scooters and there are 945 vehicles in total. How many bicycles and scooters are there in Greenville?

Answers

Answer:

Bicycles = 315

Scooters = 630, basic mathematics. The most effective method for these questions is substitution. But I might have intermingled them so double check

solve algebraically for z : 360000 + 102 = 200000 + 104z NEED ANSWER ASAP PLEASE HELP

Answers

Answer:

z = 1539.44230769

Step-by-step explanation:

360000 + 102 = 360102

360102 - 200000 = 160102

160102/104z = 1539.44230769

z = 1539.44230769

A box is to be made out of a 12 by 20 piece of cardboard. Squares of equal size will be cut out of each corner, and then the ends and sides will be folded up to form a box with an open top. Find the length L , width W , and height H of the resulting box that maximizes the volume.

Answers

Answer:

Box Dimensions:

L  = 15.15 ul

W = 7.15 ul

h = x = 2.43 ul

V(max) =    263.22 cu

Step-by-step explanation:

We call x the length of the square to be cut in the corners then:

Are of the base of the box is:

(20 - 2*x)  is the future length of the box and

(12 - 2*x) will be the width

The heigh is x  then the volume of the box is:

V = ( 20 - 2*x )* ( 12 - 2*x ) * h

And the volume as a function of x is:

V(x) = ( 20 - 2*x) * ( 12 - 2*x ) * x     or   V(x) = (240 -40*x -24*x + 4*x²) * x

V(x) =  240*x - 64*x² + 4*x³

Taking derivatives on both sides of the equation we get:

V´(x) = 240 - 128*x + 12*x²

V´(x)  =  0              240 - 128*x + 12*x²  = 0    or     60 - 32*x + 3*x²

3*x²  -  32*x  +  60  = 0

Solving:

x₁,₂  =  32  ± √ (32)² - 4*3*60 ]/ 2*3

x₁,₂  =  32  ± √ 1024 - 720 )/6

x₁,₂  = ( 32  ± √ 304 )/6

x₁,₂  = ( 32  ± 17.44 )/6

x₁  =  8.23      ( we dismiss this solution because is not feasible 2*x > 12

x₂ = 2.43  u.l ( units of length)

Then

L  =  20 - 2*x      L  = 20  - 4.85     L  = 15.15 ul

W =  12 - 2*x      W = 12 - 4.85      W = 7.15 ul

h  =  2.43 ul

V = 2.43*7.15*15.15  cubic units

V =  263.22 cu

To see if when x = 2.43   function V has a maximum we go to the second derivative

V´´(x)  = - 128  + (24)*2.43

V´´(x) = - 69.68      as        V´´(x)  < 0   then we have a maximum for V(x) in the point x = 2.43

[tex]128^3+272^3 /128^2-128*272+272^2[/tex]

Answers

wait do you want it step by step or just the answer?

the answer is 400

What is the value of the rational expression
2x+1
when x = 5?

Answers

Step-by-step explanation:

2x+1

x = 5

2(5)+1

=10+1=11

Answer:

2(5)+1

10+1

11

Hope This Helps!!!

A pyramid with a triangular base has a volume of 50cm³. If the base and the height of the triangular base are 5cm and 8cm respectively, find the height of the pyramid ? ​

Answers

Answer:

h = 7.5 cm

Step-by-step explanation:

Firstly, we find the area of the triangular base

Mathematically, we have the area of a triangle as;

A = 1/2 * b * h

A = 1/2 * 5 * 8 = 20 cm^2

Mathematically, we have the formula as;

V= 1/3 * A * h

A is base area and h is height

50 = 1/3 * 20 * h

20h = 3 * 50

20h = 150

h = 150/20

h = 7.5 cm

Given 15=3(2x+4)−3

Prove x=1

Complete the proof. Provide reasons for 1-6 below. Make sure to number your answers.

Answers

so we start by replacing x with 1 so 15=3(2•1+4)-3
we start with the inside of the para thesis so multiply 2•1 which gives us 2 and we add 4 which gives us 6
now we have 15=3(6)-3
we multiply the 3 and 6 and we get 18
Now we have 15=18-3 so we subtract 18-3 and we get 15
15=15 is the product

The value of x in the expression 15 = 3(2x + 4) - 3 is 1.

What is expression?

A number, a variable, or a combination of numbers and variables and operation symbols is called expression.

According to the given question.

We have an expression

[tex]15 = 3(2x+ 4) -3[/tex]

Solve the above expression for x.

Step 1: open the parentheses

[tex]15 = 3(2x + 4) -3[/tex]

⇒ [tex]15 = 6x + 12 -3[/tex]

Step 2: simplify the above expression.

[tex]15 = 6x + 9[/tex]

Step 3: subtract 9 to the both the sides

[tex]15 - 9 = 6x + 9 -9[/tex]

⇒[tex]6 = 6x[/tex]

Step 4: Divide both the sides by 4

⇒ [tex]\frac{6}{6} =\frac{6x}{6}[/tex]

⇒ [tex]x = 1[/tex]

Hence, we proved that x = 1 for the above expression.

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