The shortest side of a right triangle is 14 inches long. The difference between the lengths of the other two sides is 2 inches. Find the missing sides. Use exact values.

Answers

Answer 1

Answer:

The missing sides are 50 inches and 48 inches long.

Step-by-step explanation:

Let the lengths of the other two sides be x inches and y inches

And let x represent the length of the longest side.

From the question,

The difference between the lengths of the other two sides is 2 inches. That is,

x - y = 2 ...... (1)

The three sides of the right triangle are x, y, and 14 inches long.

From the Pythagorean theorem, " In a right triangle, the square of the longest side equals sum of squares of the other two sides"

Here, the longest side is x

Hence, we can write that

x² = y² + 14²

∴ x² = y² + 196 ...... (2)

Now, we have two equations, we can then solve simultaneously.

From equation (1)

x - y = 2

∴ x = y + 2 ...... (3)

Put this into equation (2)

x² = y² + 196

(y+2)² = y² + 196

y² + 4y + 4 = y² + 196

4y + 4 = 196

4y = 196 - 4

4y = 192

y = 192/4

y = 48

To determine x, we will substitute the value of y into equation (3)

x = y + 2

∴ x = 48 + 2

x = 50

Hence, x = 50 and y = 48

Since the lengths of the other two sides are x inches and y inches,

Hence, the missing sides are 50 inches and 48 inches.


Related Questions

i need helpppp again

Answers

Answer:

2/7b + 10

Step-by-step explanation:

The parabola with equation $y=ax^2+bx+c$ is graphed below:

(attached)

The zeros of the quadratic $ax^2 + bx + c$ are at $x=m$ and $x=n$, where $m>n$. What is $m-n$?

Answers

Answer:

[tex]m-n=2[/tex]

Step-by-step explanation:

Instead of using the standard form, we can use the vertex form of a quadratic equation:

[tex]f(x)=a(x-h)^2+k[/tex]

Where a is the leading coefficient, and (h, k) is our vertex.

Our vertex point is at (2, -4). So, let’s substitute 2 for h and -4 for k:

[tex]f(x)=a(x-2)^2-4[/tex]

Now, we need to determine a.

We know that it passes through the point (4, 12). So, when x is 4, y must be 12. In other words:

[tex]12=a((4)-2)^2-4[/tex]

Solve for a. Subtract within the parentheses:

[tex]12=a(2)^2-4[/tex]

Add 4 to both sides:

[tex]16=a(2)^2[/tex]

Square:

[tex]16=4a[/tex]

Solve:

[tex]a=4[/tex]

Thererfore, the value of a is 4.

So, our function is:

[tex]f(x)=4(x-2)^2-4[/tex]

Now, let’s find our roots. Set the equation to 0 and solve for x:

[tex]0=4(x-2)^2-4[/tex]

[tex]4=4(x-2)^2\\1=(x-2)^2\\x-2=\pm1 \\ x=2\pm1 \\ x=3\text{ or } 1[/tex]

So, our roots are 1 and 3.

The greater root is 3 and the lesser root is 1.

Therefore, m-n, where m>n, is 3-1 or 2.

Our final answer is 2.

Answer:

2

Step-by-step explanation:

Source: AOPS

The ratio of the angle measure of the acute angle in a right triangle is 1:3

Answers

Answer:

2:6 because 2:6 is equivalent to 1:3

Step-by-step explanation:

1x1=1 and 3x2=6

Find the exact length of the third side.
10
6
PLEASE HELP GUH

Answers

Answer:

8

Step-by-step explanation:

I'm using this equation: a^2+b^2=c^2

x^2+6^2=10^2

x^2+36+100

x^2= 64

x=sqrt64

x=8

I will give Brainlyest to the person who is first




After the temperature rose 9', the thermometer read 37°F
What is an equation that can be used to find x, the temperature before the gº increase
Drag the number, symbol, or operation sign to each box to complete the equation or symbol to

Answers

Answer:

37-9=28

Step-by-step explanation:

it was 28 F then rose 9 which is 37 so 37-9 =28

The  equation is  37 - 9= x.

What is Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides. LHS = RHS is a common mathematical formula.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given:

After the temperature rose 9°F, the thermometer read 37°F.

let  x be the temperature before the 9º increase.

So, 37 - 9= x

x= 28°F.

Hence, the equation is  37 - 9= x.

Learn more about equation here:

https://brainly.com/question/10413253

#SPJ5

4m-3(m +2) what is the answer step by step​

Answers

Answer:

-1m-6

Step-by-step explanation:

1. Multiply -3*m = -3m

2. Multiply -3* 2 = -6

3. Combine like terms : 4m + -3m = -1m

4. -1m - 6



The table shows the approximate population of Virginia for 5 years. If the trend continues, which could
be a reasonable prediction if the population in 2012?

Answers

Answer:

It is C

Step-by-step explanation:

Kevin is opening up a bookstore, where he sells both new and old books. He charges $10.75 for a new book, and $3.50 for an old book. What was Kevin's revenue last month if he sold 18 new books and 21 old books?​

Answers

The revenue last month Kevin, if he sold 18 new books and 21 old books, will be  $ 267.

What is the linear system?

A linear system is one in which the parameter in the equation has a degree of one. It might have one, two, or even more variables.

Kevin is opening up a bookstore, where he sells both new and old books.

He charges $10.75 for a new book and $3.50 for an old book.

Then the revenue last month Kevin, if he sold 18 new books and 21 old books, will be

Then the total revenue will be

Total revenue = 10.75 x 18 + 3.50 x 21

Total revenue = 193.5 + 73.5

Total revenue = $ 267

More about the linear system link is given below.

https://brainly.com/question/20379472

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A scoop of ice cream has a 3-inch diameter. How tall should the ice cream cone of the same diameter be in order to contain all of the ice cream inside the cone?

Answers

Answer:

12 inches

Step-by-step explanation:

Suppose the ice cream scoop has the shape of a sphere of a radius (r) inches.

Thus, the top of the cone will also have a radius (r) inches.

Let consider h to be the height of the cone in inches.

So, the objective is to make the volume of the scoop of the ice cream to be the same as the volume of the cone.

To do that; we need to equate both volumes together and make h the subject of the formula:

The volume of a sphere = 4/3 πr³ and the volume of a cone = 1/3πr²h

4/3 πr³  = 1/3πr²h

Multiply both sides by 3

4πr³  = πr²h

4r = h

h = 4(3)

h = 12 inches

To contain all the ice cream inside the cone, the height of the ice cream cone needs to be 12 inches tall

Compare the numbers

Answers

Answer:The answer is ≥ greater than or equal to

can you mark me Brainliest please

What is the equation for this line ?

Answers

Answer:

[tex]y = -\frac{1}{3}x + 5[/tex]

Step-by-step explanation:

y = mx + b

Let's start with where the line crosses the y axis.  We can see it crosses at 5.

So b = 5.

Let's try another point to figure out m, (3,4).

4 = 3m + 5

3m = -1

m = [tex]-\frac{1}{3}[/tex]

Answer:

y=-1/3+5

Step-by-step explanation:

since the line is going downhill, the slope would be negative (the slope is the number with the x attached). The slope is 3 over and 1 down. You would write it as rise over run, so it would be a -1/3. The line hits the y axis at 5, so the b (y=mx+b is the slope equation) would be 5.

The graph of a function f is shown below.
Find f(-2).

Answers

Answer:

-4

Step-by-step explanation:

The value of the function evaluated at [tex]x = -2[/tex] is -4.

The horizontal axis represents the set of the domain of the function, whereas the vertical axis is for the set of the range of the function. In this exercise, we need to need to find the value on the vertical axis that corresponds with a given value of the horizontal axis ([tex]x = -2[/tex]).

By direct inspection, we conclude that [tex]f(-2) = -4[/tex].

We kindly invite you to see this problem related to functions: https://brainly.com/question/12431044

How many solutions for the equation, 8x - 19 = -4 -7x

Answers

Answer: One.

Step-by-step explanation:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :   8*x-19-(-4-7*x)=0

Pull out like factors :   15x - 15  =   15 • (x - 1)

 Solve :    15   =  0

Solve  :    x-1 = 0  

 Add  1  to both sides of the

Find the rate of change of y with respect to the x of the line that passes through points (-28,8) and (-42,15)​

Answers

Answer:

-1/2

Step-by-step explanation:

8-15 = -7

-28 - -42 = 14

-7/14 = -1/2

Help me pleade help me​

Answers

The answer is C.

For a relation to be a function every x-value must be associated with one y-value. C has the x-value of 1 have two separate y-values. The others do not have an x-value that repeats.

Explain why the exponents cannot be added in the product 12^3 x 11^3?? I need a simple answer that won’t be confusing pls.

Answers

Answer:

The bases aren't the same

Step-by-step explanation:

If the bases are the same, then their exponents are added. In this case, since the exponents are the same, then 12^3*11^3=(12*11)^3=132^3=2299968

What is the domain of the following function? Show work
f(x)=(2x-1)/((2x^2)-9x+10)

Answers

Step-by-step explanation:

f ( X) = ( 2X - I ) / 2X ^ 2 - 9X + 10

= 2X-1 ) /( 2X- 5 ) ( x - 2 )

set of zeros of denominator are :

2X- 5 . = 0

X= 5/2

or

X-2=0

X=2

set of zeros of denominator = { 5/2 ,2 }

domain = R - { 5/2,2 }

Which expression does the number line represent?

NA

0

1

4

2

4

3

4

9

5

4

6

4

7

4

4

8

4

ده

9

Save and Exit

Next

Sun

Answers

Answer: D) 9 Over 4 divided by three-fourths

Step-by-step explanation:

The number line shown below is divided into 3 equal parts. To do so the highest number would have to be divided by a number that would give 3 as an answer.

Say that number is x;

x = (9/4) / 3

= 0.75

= 3/4

Number line shows 9 Over 4 divided by three-fourths .

He width of a rectangular postcard is 4 inches and the diagonal is 7.6 inches long. What is the length of the postcard? Round your answer to the nearest hundredth.

Answers

Answer:

Adjacent = x = length = 6.46 inches

Step-by-step explanation:

Given the width and diagonal of a rectangular postcard,

Find the length using Pythagoras theorem

Hypotenuse ² = opposite ² + adjacent ²

Hypotenuse = 7.6 inches

Opposite = 4 inches

Adjacent = x

Hypotenuse ² = opposite ² + adjacent ²

7.6² = 4² + x²

57.76 = 16 + x²

subtract 16 from both sides

57.76 - 16 = x²

41.76 = x²

Find the square root of both sides

x = √ 41.76

= 6.46

x = 6.46 inches

Adjacent = x = length = 6.46 inches

You and your friend went shopping. You bought 2 hats and 3 pairs of gloves for $28.25. Your friend bought 1 hat and 1 pair of gloves for $12.25. How much did one hat cost? How much did one pair of gloves cost? (Answers should reflect the real world scenario by including appropriate units.)

Answers

Answer:

One pair of gloves costs $3.75.

Step-by-step explanation:

Systems of equations

x=hats y=gloves

2x+3y=28.25  

x+y=12.25

2(12.25-y)+3y=28.25

24.5+y=28.25

y=3.75

Use a single digit times a power of 10 to estimate the number 0.00002149
please help :(

Answers

Answer:

2.149 × 10-5

Step-by-step explanation:

A cheesecake recipe says to mix 12 oz of cream cheese with 15 oz of sugar. How many ounces of cream cheese will be needed for 45 oz of sugar?​

Answers

Answer:

1.5

Step-by-step explanation:

it is one and one half, in other words.

Answer:

36 oz of cream cheese

sugar: 45 divided by 15 equals 3

12 times 3 equals 36

Rewrite the function by completing the square
f(x)=x^2-14x+63

Answers

Answer:

f(x) = (x - 7)² - 14

General Formulas and Concepts:

Pre-Algebra

Equality Properties

Algebra I

Standard Form: ax² + bx + c = 0Vertex Form: f(x) = a(bx - c)² + dCompleting the Square: (b/2)²

Step-by-step explanation:

Step 1: Define

f(x) = x² - 14x + 63

Step 2: Rewrite

Separate:                              f(x) = (x² - 14x) + 63Complete the Square:         f(x) = (x² - 14x + 49) + 63 - 49Simplify:                                f(x) = (x - 7)² - 14

Answer:

-7 and 14 on khan

Q

H.

The two-column proof below describes the statements and reasons for proving that corresponding angles are congruent:

Step

Statements

Reasons

1

UV || WZ

Given

2

Points S. Q, R, and T all lie on the same line.

Given

3

mZSQT = 180°

Definition of a Straight Angle

Angle Addition Postulate

4

m2SQV + m2VQT = m_SQT

5

Substitution Property of Equality

6

m2VQT + mZZRS = 180°

Same-Side Interior Angles Theorem

Substitution Property of Equality

7

m2SQV+mZVQT = m2VQT + mZZRS

Answers

Answer:

i can't understnd it at all i mean you organized it but what does those mean??

Step-by-step explanation:

Write an equation for the following data plz :)

Answers

Answer:

y = 4x + 1

Y values increase by 4, X values increase by 1.

M or slope, = 4/1 or 4

Y-intercept is when x = 0

When x = 0 in this case, y = 1.

So,

y = 4x +1

Answer:

y = 4x + 1

Step-by-step explanation:

This is the y = mx + b format, hopefully its useful for you! It's a linear equation because all the values grow at a constant rate.

The y-intercept is 1 and it's rise over run which means that you start at 1 on your y-intercept when graphing and then rise 4 and run 1 to the right because it's a positive slope.

Find the value of x. *

Please help

Answers

Answer:

x = 78

Step-by-step explanation:

(x-8) + 20 = 90

x - 8 = 90 - 20

x - 8 = 70

x = 70 + 8

x = 78

Check:

(78-8) + 20 = 90

70 + 20 = 90

Is the equation, y= 12x proportional or non-proportional? Explain why or why not. *

Answers

Answer:

proportional

Step-by-step explanation:

because it has a constant ratio

Answer: Proportional

Step-by-step explanation:

The equation for a proportional relationship is y=kx. This equation: y=12x fits the equation, so it's proportional.

Please solve, need help quick

Answers

Answer:

In my thought it's angle L

Step-by-step explanation:

Hope it's will help you.

Answer:

it's angle l ..................

Find the component form of the vector that represents the velocity of an airplane at the instant its wheels leave the ground, if the plane is going 75 miles per hour and the body of the plane makes an9° angle with the horizontal.

Answers

Answer:

The component form of the vector that represents the velocity of the airplane is [tex](74.1 i , \ 11.73j)\ mph[/tex]

Step-by-step explanation:

Given;

velocity of the airplane, v = 75 mph

direction of the plane, θ = 9°

The vertical component of the velocity is given by;

[tex]V_y = vsin\theta\\\\V_y = (75)(sin \ 9^0)\\\\V_y = 11.73 \ mph[/tex]

The horizontal component of the velocity is given by;

[tex]V_x = vcos \theta\\\\V_x = (75)(cos9^0)\\\\V_x = 74.1 \ mph[/tex]

Therefore, the component form of the vector that represents the velocity of the airplane is given as;

[tex](V_x , \ V_y) = (74.1 , \ 11.73)\ mph[/tex]

But all this-the mysterious, far-reaching hair-line trail, the absence of sun from the sky, the tremendous cold, and the strangeness and weirdness of it all-made no impression on the man.
What can you infer about the man from the excerpt above?

Answers

Answer:huh

Step-by-step explanation:

That the man is undaunted by the weather and is very solemn.

Explanation
If the man is completely unaffected by the bad weather that means he is very focused or serious about something.
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