What is the value of x in the diagram?

What Is The Value Of X In The Diagram?

Answers

Answer 1

Answer:

5

Step-by-step explanation:

Given is a right angled triangle.

Therefore, by Pythagoras theorem:

[tex] {(2x + 3)}^{2} = {x}^{2} + {(2x + 2)}^{2} \\ 4 {x}^{2} + 9 + 12x = {x}^{2} + 4 {x}^{2} + 4 + 8x \\ 9 + 12x = {x}^{2} + 4 + 8x \\ {x}^{2} + 4 + 8x - 12x - 9 = 0 \\ {x}^{2} - 4x - 5 = 0 \\ ({x}^{2} - 4x + 4 )- 4 - 5 = 0 \\ {(x - 2)}^{2} - 9 = 0 \\ {( x - 2)}^{2} = 9 \\ x - 2 = \pm \: \sqrt{9} \\ x - 2 = \pm 3 \\ x = 2 \pm 3 \\ x = 2 + 3 \: \: or \: \: x = 2 - 3 \\ x = 5 \: \: or \: \: x = - 1 \\ \because \: x \: can \: not \: be \: negative \\ \therefore \: x \neq \: - 1 \\ \therefore \: x = 5[/tex]


Related Questions

Which of the following was a key cause of World War II?
O A. The establishment of alliances between Japan, Russia, and Great
Britain
O B. The dangerous and aggressive expansion of totalitarian nations
O C. The Soviet Union's efforts to spread communism around the world
D. The assassination of Archduke Franz Ferdinand by Serbian
nationalists
SUBMIT

Answers

D. The Assassination of Archduke Frank Ferdinand by Serbian

Answer:

c. the dangerous and aggressive expansion of totalitarian nation

Step-by-step explanation:

you and six friends go to a movie. the tickets cost $7.50 each. you each buy a drink for $2.00 and a box of popcorn for $3.75. write an expression that represents the total amount of money spent. then evaluate the expression.

Answers

$7.25+$3.75+$2.00x6/6 = $13 each person
7.25+3.75+2.00 = $13
7.25+3.75+2.00x6 = $78
78/6 = 13

Trayvonn had 60 followers on instagram last week. now he has 12. what is the percent change?

Answers

Answer:

20%

Step-by-step

60/x%=12

12 is 1/5 of 60

1/5=20%

PLEASE HELP!!!!!

Parking for 4 hours costs $10. Parking for 5 hours costs $12. Is this a proportional relationship, and if so, what is the constant of proportionality?

Answers

Answer:

Not a Proportional Relationship ; No Constant of Proportionality

Step-by-step explanation:

Consider the first example, 4 hours of parking costs $ 10. From this we can derive the ratio 4 : 10, so that hours parked : fee for parking is a common ratio among the two examples, the other being 5 : 12;

[tex]4 : 10, Simplify\\2 : 5, Take As Fraction,\\Solution; 2 / 5ths\\[/tex]

[tex]5 : 12, Simplify\\( Can't Be Simplified Further ) - Take as Fraction,\\Solution; 5 / 12ths[/tex]

Considering that the fractions when compared are not similar, ( 2 / 5, and 5 / 12 ) they don't have a proportional relationship, and thus have no constant of proportionality

Solution; Not a Proportional Relationship

8. If Rocky Massimo's credit card has a $1,329.64 balance and he charged $528.44 in new purchases, what is the new
balance?
A $1,972.32
B $1,867.45
C$896.45
D$1,858.08
NEED ANSWERS

Answers

Answer:

D: $1,858.08

Step-by-step explanation:

if u add $1,329.64 and $528.44 then you get $1,858.08

You are given the function h(t)=t2+2t+1. Find h(−2). h (-2)=

Answers

Answer:

h(-2) = 1

Step-by-step explanation:

h(t)=t^2+2t+1

h(-2) = (-2)^2 +2(-2) +1

       = 4 -4 +1

      = 1

Answer:

-12

Step-by-step explanation:

Evaluate t - u/v when t = -1, u = -3, and v = 1/2.


P.S. it’s not multiple choice.

Answers

Hi there!

The answer would be 5.

To subtract fractions, find the LCD and then combine.

Hope this helps !

Answer:

5

Step-by-step explanation:

Use the commutative or associative property to simplify the expression.
1/3(3y)

Answers

Answer:

y

Step-by-step explanation:

Associative property is when we change the order of the bracket / can solve any order

So 1/3(3y)

= (1/3x 3)y

= 3/3y

= 1y or simply y

What is the range of the function y=*/x+8?
-00 -8 osy<00
2 sy<00

Answers

Answer:

D.

Step-by-step explanation:

(-∞, ∞) is the range of the function y = f(x) = x/2 + 8.

What is a function?

A relation is a function if it has only One y-value for each x-value.

The function y = f(x) = x/2 + 8 is a linear function with slope 1/2 and y-intercept 8.

As x varies from negative infinity to positive infinity, the value of f(x) also varies from negative infinity to positive infinity.

Therefore, the range of the function is all real numbers, that is:

y ∈ (-∞, ∞)

In interval notation, this can be written as (-∞, ∞)

Hence, (-∞, ∞) is the range of the function y = f(x) = x/2 + 8.

To learn more on Functions click:

https://brainly.com/question/21145944

#SPJ7

FInd the legth of side AB. Give your answer to 1 decimal place

Answers

Answer:

Hey love, be sure to add a photo! i will edit my answer once you do so :D

A tree harvester estimates the trunk of a tree to have a height of about 34 meters and a base diameter of about 0.52 meters. The wood of the tree has a density of about 770 kilograms per cubic meter. Find the mass of the trunk. Round your answer to the nearest hundred.

Answers

Answer: 5,559.89 kilograms

Step-by-step explanation:

Hi, to answer this question we have to apply the next formula:

Mass = π/4 (diameter) ^2 (height) (density)

Replacing with the values given and solving for M (mass)

M = π/4 (0.52) ^2 (34) (770) = 5,559.89 kg.

The mass of the trunk is 5,559.89 kilograms

Feel free to ask for more if needed or if you did not understand something.

If the sum of the measure of two angles in a triangle is 101, then the measure
of the third angle must be

Answers

Answer:

79 degrees.

Step-by-step explanation:

It is just a rule of trigonometry that all the angles inside ANY triangle will add up to 180 degrees.

There's only 3 possible angles in a triangle, so if you know what the sum of 2 are, its easy to find the last one.

All you have to do is 180 - 101, which equals 79 degrees.

Hope this helped : )

The third angle is 79
180-101=79

which linear inequality is represented by the graph?​

Answers

Answer:

y ≥ [tex]\frac{1}{3}[/tex]x - 1

Step-by-step explanation:

First, determine the slope of the line. We can see that the slope is [tex]\frac{1}{3}[/tex], because the slope has less than 1 y interval per every x interval. This means that the line is less steep. There are only 2 slope choices, [tex]\frac{1}{3}[/tex], -[tex]\frac{1}{3}\\[/tex], and 3. We can tell that the slope is positive, but it must be [tex]\frac{1}{3}\\[/tex] because it is clearly less steep than a 3 slope line.

Now, look at the portion that is shaded. It is above the line, and this means that y is greater than the equation given. We can tell it is greater than or equal to, because the line that represents the equation is shaded as well. If it was only greater than and not equal to, the line would not be shaded.

Hope this helps ! :) Please feel free to ask me any questions!

There are twelve inches in one foot, creating the equation y = 12x. If a door
frame is 6.5 feet tall, how many inches tall is it?

Answers

Answer:

78 inches.

Step-by-step explanation:

By definition, a foot is equal to 12 inches. That is modeled by the equation you wrote, y = 12x, where x is the amount of feet.

Substitute 6.5 for x. y = 12*6.5 = 78 inches.

I hope this helps!

Oscar walked at the same rate for 10.5 miles. He
completed his walk in 3 hours. What was Oscar's
rate, in miles per hour, during his walk?

Answers

Answer:

Oscar walked at the same rate for distance D =  10.5 miles.

He  completed his walk in time T = 3 hours.

=>Oscar's rate, in miles per hour, during his walk:

R = D/T = 10.5/3 = 3.5 (mile/hour)

Hope this helps!

:)

10.5 divided by 3 = 3.5 (rate)

If you have how many miles he walked and the time he completed it in; you can just divide the miles by the time to get the rate of how fast he walked those miles. This is because you have an overall mile rate and time you just need to figure out how many miles per hour which is why you divide. Think of it as a ratio 10.5:3 vs 3.5:1. Try to get the right side of the ration down to 1 by dividing both sides by the right side.


Hope this helps, sorry I’m bad at explaining

How do I work out this question (explanation and answer please)

Answers

Answer: Each friend will pay £3.75

Step-by-step explanation:

4 friends pay £15, 12 will pay

12/4 x 15 = £45

Each will pay 45/12 = £3.75

Which is the graph of the function f(x) = x3 – x2 – 17x - 15?

Answers

Answer with Step-by-step explanation:

We are given that a function

[tex]f(x)=x^3-x^2-17x-15[/tex]

We have to find the graph of the given function.

y-intercept:It is that  value of y where the graph cut the y- axis.

Let

[tex]y=f(x)=x^3-x^2-17x-15[/tex]

Substitute x=0

Then, we get

[tex]f(0)=-15[/tex]

y-intercept of the graph=-15

x- intercept: It is that value of x where the graph cut the x- axis.

Substitute y=0

[tex]x^3-x^2-17x-15=0[/tex]

Substitute x=-1

[tex]-1-1+17-15=0[/tex]

Therefore,x=-1  is a solution of given equation.

[tex](x+1)(x^2-2x-15)=0[/tex]

[tex](x+1)(x^2-5x+3x-15)=0[/tex]

[tex](x+1)(x(x-5)+3(x-5))=0[/tex]

[tex](x+1)(x+3)(x-5)=0[/tex]

[tex]\implies x=-1,-3,5[/tex]

Hence, the x-intercept are

-3,-1 and 5

Answer:b on edg 2020

Step-by-step explanation:

The ratio of boys to girls at Jackie Chan high school is 5:3. If there are a total of 250 boys in the school how many girls are in the school?

Answers

Answer:

150

Step-by-step explanation:

As the ratio is 5:3 ,

Number of boys / number of girls = 5 / 3

250 / number of girls = 5 / 3

Number of girls = 250 × 3/5

Number of girls = 150

Amber's mean mark on five tests is 80.
Her marks on four of these tests are 68, 81, 74 and 89.
Work out her mark on the fifth test.

Answers

Answer:

The answer is 88.

Step-by-step explanation:

68+81+74+89+x/5=80

312+x/5=80

312+x=80*5

312+x=400

x=400-312

x=88

Answer:

88

Step-by-step explanation:

The mean is the total sum of all the marks divided by how many there are.

68+81+74+89=312 Total of 4 tests

80×5 = 400 Total marks on 5 tests

400-312 = 88 Total marks on 5 tests - Total marks on 4 tests = 1 test

68+81+74+89+88 = 400

What is the equation of the parabola with focus (-2, 2) and directrix y = -1?

Answers

Answer:

(x+2)^2=6(y-1/2)

Step-by-step explanation:

Which shape has only acute angles?

Answers

Answer:

Triangle

Step-by-step explanation:

Pls mark as brainliest

Answer:

triangle

Step-by-step explanation:

The rectangle and arrow both have right angles, so they are crossed out. The pentagon has obtuse angles, so it is also not the answer

Write as a product

(a+1)^3+x^3

Answers

Answer:

Variables

Any lowercase letter may be used as a variable.

Exponents

Exponents are supported on variables using the ^ (caret) symbol. For example, to express x2, enter x^2. Note: exponents must be positive integers, no negatives, decimals, or variables. Exponents may not currently be placed on numbers, brackets, or parentheses.

Parentheses and Brackets

Parentheses ( ) and brackets [ ] may be used to group terms as in a standard equation or expression.

Multiplication, Addition, and Subtraction

For addition and subtraction, use the standard + and - symbols respectively. For multiplication, use the * symbol. A * symbol is not necessary when multiplying a number by a variable. For instance: 2 * x can also be entered as 2x. Similarly, 2 * (x + 5) can also be entered as 2(x + 5); 2x * (5) can be entered as 2x(5). The * is also optional when multiplying with parentheses, example: (x + 1)(x - 1).

Order of Operations

The calculator follows the standard order of operations taught by most algebra books - Parentheses, Exponents, Multiplication and Division, Addition and Subtraction. The only exception is that division is not currently supported; attempts to use the / symbol will result in an error.

Division, Square Root, Radicals, Fractions

The above features are not supported.

Step-by-step explanation:

I need help with this math problem.

Answers

Answer:

(45,60)

Step-by-step explanation:

in a parallelogram, opposite angles are equal measure

2x-10 = y + 20

angles that lie on the same line add up to 180, since alternate angles of parallel lines and a transversal are equivalent

2x + 10 + 2x - 10 = 180

solving the equation with only Xs

4x = 180

x = 180/4 = 45

plug x = 45 into x and y equation

90-10 = y+ 20

80 = y + 20

y = 80-20 = 60

Lina owns 300 shares of General Motors Company. She receives annual dividends of $0.54 per share. How much will she received in dividend payments? *

Answers

Answer:

The total payment is $162.00

Step-by-step explanation:

Take the number of shares time the amount per share

300 * .54

162

The total payment is $162.00

Which table has a constant of proportionality between y and x of 4?

Answers

Answer:

Answer A

Step-by-step explanation:

16 / 4 = 4

36 / 9 = 4

64 / 16 = 4

Note that the symbol / is the equivalent of the division sign in math.

Answer:

A <3

Step-by-step explanation:

Plzzzz help
Plzz help

Answers

Answer: It starts at 2.5, and ends at 8.5.

Step-by-step explanation:

Answer:

range = 6

Step-by-step explanation:

The range = maximum value - minimum value

maximum value = 8.5 and minimum value = 2.5 ( indicated by the dots )

range = 8.5 - 2.5 = 6

ignore circled one and work it out please​

Answers

Answer:

a. [tex]\frac{(x-7)}{x^2+x-30}[/tex]

Step-by-step explanation:

[tex]\huge \frac{x^2-3x-28}{(x^2+10x+24)(x-5)} \\\\\huge {=\frac{x^2-7x+4x-28}{(x^2+6x+4x+24)(x-5)}}\\\\\huge {=\frac{x(x-7)+4(x-7)}{\{x(x+6)+4(x+6)\}(x-5)}}\\\\\huge {=\frac{(x-7)(x+4)}{(x+6)(x+4)(x-5)}}\\\\\huge {=\frac{(x-7)}{(x+6)(x-5)}}\\\\\huge {=\frac{(x-7)}{x^2+(6-5)x+6(-5)}}\\\\\huge {=\frac{(x-7)}{x^2+x-30}}[/tex]

Which equation represents the data in this function table?

OA) y = x + 2
OB) x = y + 2
OC) y = 2x
OD) x = 2y

Answers

Answer:

c

Step-by-step explanation:

its not too complicated, look

to get from 2 to 5 u gotta multiply by 2

so C is saying that Y equals 2 times X which would be: 4 equals 2 times 2

Or 12 equals 2 times 6

Answer:

C

Step-by-step explanation:

Rise over run is [tex]\frac{12-4}{6-2} = \frac{8}{4}=2[/tex]

so y=2x

The table shows the proportional relationship between the time in hours (h) Sara babysits and the amount in dollars (a) Sara earns babysitting.
h a
2 8
3 12
4 16
5 20
The equation a = 5h shows the relationship between the amount in dollars (a) Abbey earns babysitting and the time in hours (h) Abbey babysits.

Which statement correctly identifies who earns more and how much more she earns?
A
Sara earns $1 more per hour than Abbey.

B
Sara earns $4 more per hour than Abbey.

C
Abbey earns $1 more per hour than Sara.

D
Abbey earns $5 more per hour than Sara.

Answers

Answer:

C

Step-by-step explanation:

The table shows that Sara earns 4 dollars per hour. The equation shows that Abbey earns 5 dollars per hour.

I hope that helps. If there are any questions left, just comment:)

Please mark me brainliest (it gets you 10 points back btw)



A reindeer runs
20 1/4 miles in 3 hours. At that rate, how many miles does it run in 1 hour?
-must haves...
right answer.
makes sense.
step by step.
^can you guys please help me make sure I got my answer right, thank youu;)
(choices of the answers: 3 1/4; 6 3/4; 12 1/4; 60 3/4)

Answers

Answer:

6 3/4 miles

Step-by-step explanation:

We can use ratios to solve

20.25 miles         x miles

------------------ = ------------

3 hours              1 hours

Using cross products

20.25 * 1 = 3x

Divide each side by 3

20.25 /3 = x

6.75 = x

Changing to a fraction

6 3/4

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