Mathematics Middle School

Two sides of a triangle have the same length. The third side measures 2 m less than twice the common length. The perimeter of the triangle is 26 m. What are the lengths of the three sides?

Answers

Answer 1

Final answer:

The lengths of the three sides of the triangle are 7m, 7m, and 12m.

Explanation:

Let the length of the two equal sides be 'x'.

The third side measures 2m less than twice the common length, so it is (2x - 2)m in length.

Given that the perimeter of the triangle is 26m, we can set up the equation:

x + x + (2x - 2) = 26

Simplifying the equation:

4x - 2 = 26

4x = 28

x = 7

So, the lengths of the three sides are 7m, 7m, and (2x - 2)m = (2 * 7 - 2)m = 12m.

Learn more about Triangle side lengths here:

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Answer 2

Final answer:

The triangle with two sides of equal length and a perimeter of 26 m has sides measuring 7 m, 7 m, and 12 m.

Explanation:

To solve for the lengths of the sides of the triangle described in the question, we can set up an equation based on the information given. Since two sides of the triangle have the same length, we can call that common length 'x'. The third side is described as being '2 m less than twice the common length', which can be written as '2x - 2'. The perimeter of the triangle, which is the sum of the lengths of all sides, is given as 26 m.

Therefore, the perimeter equation would be:

x + x + (2x - 2) = 26

This simplifies to:

4x - 2 = 26

Adding 2 to both sides, we get:

4x = 28

Dividing both sides by 4, we find x:

x = 7

Now we know that the two sides of equal length are both 7 m, and the third side is:

2x - 2 = 2(7) - 2 = 12

So the lengths of the three sides of the triangle are 7 m, 7 m, and 12 m.

Related Questions

2x-7 divided by 6x squared -37x+56

Answers

Answer:

the 6.192# melebulated by 59 and devide it by 597 your answere is 64

Step-by-step explanation:

For the function f defined by f(x)=3x2−2x+5 find f(−x),−f(x) , and −f(−x).

Answers

Step-by-step explanation:

[tex]f(x)=3x^2-2x+5\\\\f(-x)=\text{substitute (-x) instead x in f(x)}\\\\f(-x)=3(-x)^2-2(-x)+5=3x^2+2x+5\\\\-f(x)=-(3x^2-2x+5)=-3x^2-(-2x)-5=-3x^2+2x-5\\\\-f(-x)=-(3x^2+2x+5)=-3x^2-2x-5[/tex]

The answers are:

[tex]\begin{aligned}& f(-x)=3 x^2+2 x+5 \\& -f(x)=-3 x^2+2 x-5 \\& -f(-x)=-3 x^2-2 x-5\end{aligned}[/tex]

Let's find f(−x), −f(x), and −f(−x) for the given function [tex]f(x)=3 x^2-2 x+5[/tex].

f(−x):

Replace x with −x in the function:

[tex]f(-x)=3(-x)^2-2(-x)+5[/tex]

Simplify this expression:

[tex]f(-x)=3 x^2+2 x+5[/tex]

−f(x):

Multiply the entire function f(x) by −1:

[tex]-f(x)=-\left(3 x^2-2 x+5\right)[/tex]

Distribute the negative sign:

[tex]-f(x)=-3 x^2+2 x-5[/tex]

−f(−x):

Replace x with −x in the function f(x) and then multiply the whole expression by −1:

[tex]-f(-x)=-\left(3(-x)^2-2(-x)+5\right)[/tex]

Simplify this expression:

[tex]-f(-x)=-\left(3 x^2+2 x+5\right)[/tex]

Distribute the negative sign:

[tex]-f(-x)=-3 x^2-2 x-5[/tex]

Question:

For the function f defined by [tex]f(x)=3 x^2-2 x+5[/tex] find f(−x),−f(x) , and −f(−x).

What is the measure of AC?

Answers

Answer:

AC = 52.8

Step-by-step explanation:

33/20 = 1.65

12*1.65 = 19.8

BA = 19.8

CB + BA = AC

33 + 19.8 = 52.8

Answer:

AC = 52.8

Step-by-step explanation:

Since BE is parallel to CD and intersects the 2 sides of the triangle then it divides those sides proportionally, that is

[tex]\frac{BC}{AB}[/tex] = [tex]\frac{DE}{AE}[/tex], substituting values

[tex]\frac{33}{AB }[/tex] = [tex]\frac{20}{12}[/tex] ( cross- multiply )

20AB = 396 ( divide both sides by 20 )

AB = 19.8

Thus

AC = AB + BC = 19.8 + 33 = 52.8

A moose population is growing exponentially following the pattern in the table shown below. Assuming that the pattern continues, what will be the population of moose after 12 years? Show all your work! Round your answer to the nearest whole number. (5 points)
Time (year) Population
0 40
1 62
2 96
3 149
4 231

Answers

Answer:

The population of moose after 12 years will be 7,692

Step-by-step explanation:

we know that

In this problem we have a exponential function of the form

[tex]y=a(b^x)[/tex]

where

y ----> population of moose

x ----> the time in years

a is the y-intercept or initial value

b is the base of the exponential function

we have

[tex]a=40[/tex] ----> the y-intercept is given in the table (value of y when the value of x is equal to zero)

substitute

[tex]y=40(b^x)[/tex]

Find the value of b

For x=1, y=62

substitute in the equation

[tex]62=40(b^1)\\b=62/40\\b=1.55[/tex]

therefore

[tex]y=40(1.55^x)[/tex]

What will be the population of moose after 12 years?

For x=12 years

substitute in the exponential equation

[tex]y=40(1.55^{12})[/tex]

[tex]y=7,692[/tex]

NEED HELP ASPA PLS HELP WITH THIS

Answers

SEE IMAGE FOR A, B, C, D REFERENCE

A- 3

B- 3

C- 6

D- 3x+6

On the board you should have 6 of the orange + tiles and 3 of the orange x tiles.

a _____ angle has the same measure as its arc.

Answers

Answer:

central

Step-by-step explanation:

greetings the correct answer is central odyssey ware

EUREKA MATH kATRINA HAS 23 STICKERS AND JENNIFER HAS 9. HOW MANYMORE STICKERS DOES JENNIFER NEED TO HAVE AS MANY AS KATRINA?

Answers

Answer:

Step-by-step explanation:

23 - 9 = 14

Answer:

Step-by-step explanation:

23-9=14

What is the quotient when the decimal number 10 and 6/10 is divided by four hundredths

A) 265
B) 265.2
C) 26.25
D) 26.52

Answers

Answer:

Step-by-step explanation:

10 and 6/10 = 10.6

4 hundredths = 4/100 = 0.04

10.6 / 0.04 = 265 <==

Square root of one hundred and twenty three

Answers

The square root is 11.0905.

The square root is 11.0905365064

Two communications companies offer calling
plans. With Company X, it costs 35¢ to connect
and then 5¢ for each minute. With Company Y,
it costs 15¢ to connect and then 4¢ for each
minute.
Write and simplify an expression that represents
how much more Company X charges than
Company Y, in cents, for n minutes.

Answers

Answer:

(20 + n)¢

Step-by-step explanation:

With Company X, it costs 35¢ to connect and then 5¢ for each minute.

So, for n minutes of calling the company X charges, C(x) = (35 + 5n)¢

Again, With Company Y, it costs 15¢ to connect and then 4¢ for each minute.

So, for n minutes of calling the company Y charges, C(y) = (15 + 4n)¢.

Therefore, the company Y charges for n minutes of calling less than company X is [(35 + 5n) - (15 + 4n)]¢ = (20 + n)¢ (Answer)

Final answer:

To find how much more Company X charges than Company Y for n minutes, subtract the cost of Company Y from the cost of Company X. The expression to represent the difference in charges is 0.2 + 0.01n.

Explanation:

To find how much more Company X charges than Company Y, we need to subtract the cost of Company Y from the cost of Company X for n minutes.

Let's denote the cost of Company X as CX and the cost of Company Y as CY.

For Company X, the cost is $0.35 to connect and $0.05 for each minute. So, the cost of CX for n minutes is given by CX = 0.35 + 0.05n.

Similarly, for Company Y, the cost is $0.15 to connect and $0.04 for each minute. So, the cost of CY for n minutes is given by CY = 0.15 + 0.04n.

To find the difference in charges, we subtract CY from CX:

Company X charges (CX - CY) = (0.35 + 0.05n) - (0.15 + 0.04n) = 0.2 + 0.01n

(3-20i)-(14+6i)-(8-2i)

Answers

Because there are parentheses we distribute the negative signs:

3 - 20i + (-14) - 6i + (-8) + 2i

Next combine like terms:

3 + (-14) + (-8) and -20i - 6i + 2i

-19 -24i

A hamster runs at a speed of 17 centimeters per second in a wheel of radius 10 centimeters angular velocity and how fast will the wheel spin in revolutions per minute

Answers

Answer:

3.229 revolutions per minute

Step-by-step explanation:

The angular velocity of an object is the rate at which it rotates around a fixed axis. In this case, the hamster wheel is rotating.

To find the angular velocity of the wheel, we need to convert the linear velocity of the hamster into angular velocity.

The linear velocity of the hamster is given as 17 centimeters per second. This means that for every second, the hamster moves 17 centimeters along the circumference of the wheel.

To find the angular velocity, we need to find the distance traveled along the circumference of the wheel in one revolution. The circumference of a circle is given by the formula C = 2πr, where r is the radius of the wheel.

In this case, the radius of the wheel is 10 centimeters. So, the circumference of the wheel is C = 2π(10) = 20π centimeters.

Since the hamster runs at a speed of 17 centimeters per second, in one revolution of the wheel, it covers a distance of 20π centimeters.

Now, we can find the angular velocity by dividing the linear velocity by the distance traveled in one revolution.

Angular velocity = linear velocity / distance traveled in one revolution

Angular velocity = 17 centimeters per second / (20π centimeters per revolution)

Simplifying the expression, we get:

Angular velocity = 17 / (20π) revolutions per second

To convert the angular velocity from revolutions per second to revolutions per minute, we need to multiply it by 60 (since there are 60 seconds in a minute).

Angular velocity in revolutions per minute = (17 / (20π)) * 60

Calculating the value, we get:

Angular velocity in revolutions per minute ≈ 3.229 revolutions per minute

Therefore, the wheel will s

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