A sling is in the shape of an isosceles triangle with a perimeter of 155 inches. The longest side of the sling is 14 inches longer than either of the other two sides. Find the lengths of each side.

Answers

Answer 1

Hello there.

To answer this question, we need to remember some properties of the isosceles triangle.

First (and most importantly), an isosceles triangle is composed by three sides, in which only two of the sides have equal length.

The perimeter of a triangle is given by the sum of the lengths of the sides, such that: \(2p={\ell}_1+{\ell}_2+{\ell}_3\), in which \(p\) is the semiperimeter.

Given that the perimeter of such triangle is equal to \(155~\text{in}\) and the longest side is \(14~\text{in}\) longer than both the other sides, we have that:

\(\begin{cases}{\ell}_2={\ell}_3\\ {\ell}_1+{\ell}_2+{\ell}_3=155\\ {\ell}_1={\ell}_2+14\\\end{cases}\)

Using these informations, in terms of \({\ell}_2\), we get:

\({\ell}_2+14+{\ell}_2+{\ell}_2=155\)

Sum the equal terms on the left hand side of the equation

\(3\,{\ell}_2+14=155\)

Subtract \(14\) on both sides of the equation

\(3\,{\ell}_2=141\)

Divide both sides of the equation by a factor of \(3\)

\({\ell}_2=47~\text{in}\)

Substituting this value on the first and second equations, we get:

\({\ell}_3=47~\text{in}\\\\\\ {\ell}_1=47+14=61~\text{in}\)

Thus, the length of the sides of this triangle are, respectively from the largest to the smallest: \({\ell}_1=61~\text{in},~{\ell}_2=47~\text{in},~{\ell}_3=47~\text{in}~~\checkmark\)

These are the values we were searching for.


Related Questions

35.7 divided by 0.07
486.12 divided by 0.6
3.43 divided by 0.035
5,418.54 divided by0.009
812.5 divided by 1.25

Answers

Answer:

510, 810.2, 98, 602.06, 650

Step-by-step explanation:

its in the order as you put hope I got them right sorry if I messed up :)

Answer:

1.) 510

2.) 810.2

3.) 98

4.) 555.556

5.) 650

Katie, William, and Katherine go to the mall with $25.00. Katie wants a shirt that costs $9.78. William wants a hat that costs $5.99. Katherine wants a pair of sunglasses that costs $10.45.

Answers

Answer:

What is the question?

Step-by-step explanation:

They would spend $26.22 if they bought all three items.


Write an equation in slope-intercept form for the line with slope
-1/4
and y-intercept 4.

Answers

Answer:

4

Step-by-step explanation:

The equation of the line is written in the slope-intercept form, which is: y = mx + b, where m represents the slope and b represents the y-intercept. In our equation, y = − 7 x + 4 , we see that the y-intercept of the line is 4.

Add me brainiest

Answer:

Scientific research

Step-by-step explanation:

I don't know answer sorry mL nalang tayo

help me please please please

help me please please please

Answers

The angle measures for this problem are given as follows:

a = 62º.b = 118º.c = 62º.d = 62º.

How to obtain the angle measures?

The sum of the measures of the internal angles of a triangle is of 180º.

The triangle in this problem is ABC, hence the measure of a is obtained as follows:

a + 68 + 50 = 180

a = 180 - (68 + 50)

a = 62º.

c and d are corresponding angles to angle a, as they are on the same position relative to parallel lines, hence their measures are given as follows:

c = 62º.d = 62º.

Angle b is a corresponding interior angle with angle a, hence they are supplementary and it's measure is given as follows:

a + b = 180

62 + b = 180

b = 118º.

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1
Given: - 2 x > 6.
Choose the solution set.
O{x|xER, x>-12}
{x|xER, x>-3}
{x|xER,x<-3}
(xxER, x < -12}

1Given: - 2 x &gt; 6.Choose the solution set.O{x|xER, x&gt;-12}{x|xER, x&gt;-3}{x|xER,x&lt;-3}(xxER,

Answers

Answer:

x< -12

Step-by-step explanation:

-1/2x>6
x-2.   x-2

x>-12

Since we multiply by we negative we flip the sign

x< -12

Hopes this helps

HELP THIS IS DUE TODAY!Rectangle A measures 9 inches by 3 inches. Rectangle B is a scaled copy of Rectangle A. Select all of the measurement pairs that could be the dimensions of Rectangle B. *
5 points
4.5 inches by 1.5 inches
8 inches by 2 inches
10 inches by 4 inches
13.5 inches by 4.5 inches
90 inches by 30 inches

Answers

Answer:

1. 90 in. by 30 in.

2. 4.5 in. by 1.5 in.

3. 13.5 inches by 4.5

Those are the 3 correct answers.

A puzzle has 1080 pieces. How many pieces are 80% of the puzzle?

Answers

864 because 1080 times .80 is 864

Answer:

864

Step-by-step explanation:

80/100 simplified is 4/5

so you do 4/5 of 1080

which is 1080 divided by 5 that is 216

and then 216 x 4 which is 864

3.6 subtract by 1.487 is egual to ______.Pls write in step by step.​

Answers

Answer:

2.113

Step-by-step explanation:

 

               \(3.600\\1.487 \ -\\\overline{2.113}\)

e
B
0
14. The table shows the number of inches of
rain over five months. What would be an
appropriate display of the data? Explain.
(Lesson 2)
Month
Number
of Inches
of Rain
Jan. Feb. Mar.
1.5
2.2
3.6
Apr.
5.3
May
4.8

eB014. The table shows the number of inches ofrain over five months. What would be anappropriate display

Answers

The graph of the given function is attached.

Given is a function for the rainfall in 5 months in inches.

We need to display the data,

So, as we can see that the data is not showing any proportion or pattern,

So, it can be displayed as a line chart.

Hence the chart is attached for the function.

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eB014. The table shows the number of inches ofrain over five months. What would be anappropriate display

janice spent 3.85 for 2 pounds of apples and 3 pounds of pairs. lisa spent 4.94 for 4 pounds of apples and 2 pounds of pairs. how much does a pound of apples cost

Answers

Based on a system of equations, a pound of apples costs $0.89.

What is a system of equations?

A system of equations is two or more equations solved at the same time or concurrently.

A system of equations is also referred to as simultaneous equations.

                    Apples     Pears     Total Cost

Janice              2              3             $3.85

Lisa                  4              2             $4.94

Let the cost of a pound of apples = x

Let the cost of a pound of pears = y

Equations:

2x + 3y = 3.85 ... Equation 1

4x + 2y = 4.94 ... Equation 2

Multiply Equation 1 by 2:

4x + 6y = 7.7 ... Equation 3

Subtract Equation 2 from Equation 3:

4x + 6y = 7.7

-

4x + 2y = 4.94

4y = 2.76

y = 0.69

Substitute y = 0.69 in Equation 1 or 2:

4x + 2y = 4.94

4x + 2(0.69) = 4.94

4x + 1.38 = 4.94

4x = 3.56

x = 0.89

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How do you write 0.166666 as a fraction

Answers

Answer:

16/1000000

Step-by-step explanation:

The scale of a map says that 2 inches represents 5 miles. What distance on the map ---- in inches ----- represents an actual distance of 6 miles?

Answers

Answer:

2.4 inches on the map

Step-by-step explanation:

2/5 = x/6

2/5 • 6 = x/6

2.4 = x

The distance on the map 2.4  inches represents an actual distance of 6 miles.

What is scale factor?

A scale factor in math is the ratio between corresponding measurements of an object and a representation of that object.

Now it is given that,

The scale of a map says that 2 inches represents 5 miles.

So, we can write

2 inches = 5 miles

⇒ 1 Mile = 2/5 inches

Hence, 6 Mile = 6 * 2/5 inches

6 Mile = 12/5 inches

6 Mile = 2.4 inches

Thus, the distance on the map 2.4  inches represents an actual distance of 6 miles.

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Which is the graph of linear inequality x - 2y 2-12?
10
10
10
1034
Help asappp!!!pls

Answers

It would have to have a positive slope and the bottom needs to be shaded, since -2y is negative it means we will be dividing by a negative. The inequality sign will switch.

also if it is < then the line is dotted, if it’s the “greater or equal to sign” then the line is not dotted.

dunno if I explained it very well

The shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.

What is inequality?

An inequality is used to compare two or more expressions or numbers.

For example -

2x > 4y + 3

x + y > 3

x - y < 6

Given is the inequality as -

x - 2y² < 12

The given inequality is -

x - 2y² < 12

2y² - x < - 12

2y² < x - 12

y² < (x/2) - 6

\($y < \pm\sqrt{\frac{x}{2}-6 }\)

\($y < \sqrt{\frac{x}{2}-6 }\)        

and

\($y < -\sqrt{\frac{x}{2}-6 }\)

Refer to the graph of the equation attached. The shaded region common to both the inequalities represents the solution set of the inequality.

Therefore, the shaded region common to both the inequalities represents the solution set of the inequality → x - 2y² < 12.

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Which is the graph of linear inequality x - 2y 2-12?1010101034Help asappp!!!pls

mark is shopping during a computers store 20% sale. He wants to buy computers in the range of $500 to $1000. how much are the computers after 20%

Answers

It's £2000    ( don't have the us money sign sorry )

The cost of computer($1000) after sale is $800.

Given that, a computers store 20% sale. He wants to buy computers in the range of $500 to $1000.

What is percentage?

Percentage is defined as a given part or amount in every hundred. It is a fraction with 100 as the denominator and is represented by the symbol "%".

If cost of computer is $500

Then, 20% of 500 = 0.2×500

= $100

So, after sale the cost of computer is 500-100=$400

Similarly, for other cost as well

If cost of computer is $1000

Then, 20% of 1000 = 0.2×1000

= $200

So, after sale the cost of computer is 1000-200=$800

Therefore, the cost of computer($1000) after sale is $800.

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Graph the image of this figure after a dilation with a scale factor of 2 centered at the origin.
Use the polygon tool to graph the dilated figure.
Polygon
-10 -9
+Move
10
9
8-
-8 -7 -6 -5 -4 -3 -2 -19
-2
Undo
2 3 4
Redo
5
6
x Reset
00
9
10

Graph the image of this figure after a dilation with a scale factor of 2 centered at the origin.Use the

Answers

The image of the figure after the dilation is added as an attachment

Graphing the image of the figure after the dilation

From the question, we have the following parameters that can be used in our computation:

Scale factor = 2 centered at the origin.

The coordinates of the figure are

(2, 2), (2, 5), (-2, 2) and (-2, 5)

When dilated by 2 centered at the origin, we have

Image = Points * 2

Substitute the known values in the above equation, so, we have the following representation

Image = (2, 2), (2, 5), (-2, 2) and (-2, 5) * 2

Evaluate

Image = (4, 4), (4, 10), (-4, 4) and (-4, 10)

The graph is added as an attachment

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Graph the image of this figure after a dilation with a scale factor of 2 centered at the origin.Use the

HELP PLEASE QUICK
use the graphs of f and g to describe the transformation from the graph of f to the graph of g.


f(x)=2x+3

g(x)=f(x)-2

Answers

Answer:

2x - 1

Step-by-step explanation:

that is the procedure above

HELP PLEASE QUICKuse the graphs of f and g to describe the transformation from the graph of f to the

What is 45 equivalent to in ratios

Answers

Answer:

45/100   IS 45%

Step-by-step explanation:

While driving your rental car on your vacation in Europe, you find that you are getting 13.3 km/of gasolineWhat does this value correspond to in miles per gallon?

13.3km/L=__________mi/gal

Answers

The rental car is getting approximately 37.56 miles per gallon.

To convert kilometers per liter (km/l) to miles per gallon (mpg), you can use the following conversion factor:

1 km/l ≈ 2.82475 mpg

Therefore, if your rental car is getting 13.3 km/l of gasoline, the equivalent value in miles per gallon would be:

13.3 km/l x 2.82475 mpg ≈ 37.56 mpg

So, your rental car is getting approximately 37.56 miles per gallon.

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Bookwork code: N84
Look at the poster below showing the price of pencils in a stationery shop.
Annabel wants to buy exactly 76 pencils. What is the lowest amount she can
pay?
Give your answer in pounds (£).
spar
..
Pencils for sale!

30p each

Pack of 10
pencils for £2

Answers

Based on mathematical operations, the lowest amount that Annabel can pay for pencils is $15.20

How is the lowest amount determined?

The lowest amount that Annabel can pay for pencils can be determined using the mathematical operations of multiplication and division.

Multiplication and division are two of the four basic mathematical operations, including addition and subtraction.

If Annabel chooses to purchase the first pencil at 30p each, she would pay £22.80 (£0.30 x 76).

If Annabel chooses to purchase the second pencil class of a pack of 10 pencils for £2, she would pay £15.20 [£2 x (76 ÷ 10)].

Pencils for sale

30p each

Pack of 10 pencils for £2

Thus, if Annabel wants to buy the pencils, she can either pay £15.20 or £22.80, but using mathematical operations, the lowest amount she can pay is £15.20.

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Given f (x) = x2 + 6x + 5 and g(x) = x3 + x2 − 4x − 4, find the domain of f over g of x period

{x ∈ ℝ}
{x ∈ ℝ| x ≠ −5}
{x ∈ ℝ| x ≠ −1, −2, 2}
{x ∈ ℝ| x ≠ −2, 2}

Answers

The main limiting issue with the domain this function is potentially picking an x-value that makes that denominator equal 0, because dividing by 0 is bad.

So, the domain will be all real numbers, except for those that make g(x)=0.

g(-1) = 0, g(-2)=0, and g(2) = 0, so -1, -2, and 2 must be excluded from the domain.

Your answer is {x ∈ ℝ| x ≠ −1, −2, 2}.

Answer:

\(\textsf{Domain}: \quad \{ x \in \mathbb{R}\;|\;x \neq -1, -2, 2\}\)

Step-by-step explanation:

Given functions:

\(\begin{cases} f(x)=x^2+6x+5\\g(x)=x^3+x^2-4x-4\end{cases}\)

Factor function f(x):

\(\begin{aligned}\implies f(x)&= x^2+6x+5\\&=x^2+x+5x+5\\&=x(x+1)+5(x+1)\\&=(x+5)(x+1)\end{aligned}\)

Factor function g(x):

\(\begin{aligned}\implies g(x)&=x^3+x^2-4x-4\\&=(x+1)(x^2-4)\\&=(x+1)(x+2)(x-2)\end{aligned}\)

Therefore the composite function is:

\(\implies \dfrac{f(x)}{g(x)}=\dfrac{(x+5)(x+1)}{(x+1)(x+2)(x-2)}\)

A rational function is undefined when the denominator equals zero.

Therefore, the given composite function is undefined when (x+1)(x+2)(x-2)=0:

\(x+1=0 \implies x=-1\)\(x+2=0 \implies x=-2\)\(x-2=0 \implies x=2\)

The domain of a function is the set of all possible input values (x-values).

Therefore, as the composite function is undefined when x = -1, x = -2 and x = 2, the domain is:

\(\{ x \in \mathbb{R}\;|\;x \neq -1, -2, 2\}\)

Quiana measures the width of her doorway entrance using a measuring tape.She measures the width as 33 inches. She later finds a better tape measure that measures to the nearest half of an inch. After re-measuring,she determines that the actual measure of the doorway is 32 1/2 inches

Answers

1.2 and 1.2 and not to mention a fat 1.2 sheesh that’s pretty good 1.2

Julio tiene 12 años de edad y su padre tiene 42 años. ¿Cuántos años tendrá Julio cuando su padre tenga el doble de su edad?

Answers

Julio will be 30 years old when his father is twice his age.

To determine the age at which Julio will be twice his father's age, we need to find the age difference between them and then add that difference to Julio's current age.

Currently, Julio is 12 years old, and his father is 42 years old. The age difference between them is 42 - 12 = 30 years.

For Julio to be twice his father's age, the age difference needs to remain the same as it is currently. Therefore, when Julio is x years old, his father will be x + 30 years old.

Setting up an equation to solve for x:

x + 30 = 2x

Simplifying the equation, we subtract x from both sides:

30 = x

Thus, when Julio is 30 years old, his father will be 30 + 30 = 60 years old. At this point, Julio will indeed be twice his father's age.

Therefore, Julio will be 30 years old when his father is twice his age.

Note : the translated question is Julio is 12 years old and his father is 42 years old. How old will Julio be when his father is twice his age?

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You receive 5 bonus points in class Wright an integer to represent that

Answers

Answer:

to represent what-

Step-by-step explanation:

You sailed 0.055 units to the left and found treasure at 0.085 units find where the ship started

Answers

The ship started at the Position 0.14 units.

To determine the starting position of the ship, we can consider the distance sailed to the left and the distance to the treasure.

Given that you sailed 0.055 units to the left and found the treasure at 0.085 units, we can represent this situation mathematically as follows:

Starting position + Distance sailed to the left = Distance to the treasure

Let's assign a variable, "x," to represent the starting position of the ship.

The equation becomes:

x - 0.055 = 0.085

To find the value of x, we can solve this equation by isolating x on one side:

x = 0.085 + 0.055

x = 0.14

Therefore, the ship started at the position 0.14 units.

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Find the product. Enter your final answer as a simplified fraction.
-1/8•7•2/5=

Answers

Answer:

-7/20  

Step-by-step explanation:

Answer:

-1/140

Step-by-step explanation:

-1/8*7*2/5

-7/8*2/5

-7/20

There are 7 girls and 9 boys on a playground.

What is the ratio of the number of girls to the total number of children?

Enter your answer by filling in the boxes

Answers

Answer:

7:16

Step-by-step explanation:

The answer will be laid out like this-

girls : total children

This question is asking for the ratio of girls to the total number of kids, and we already know that there are 7 girls, so that already fills in the first part of the answer! Now we have to add both the girls and the boys up for the rest of the answer.

7 + 9 = 16

Now we just fill in the blanks for the layout we just created and we have our answer- 7:16!

Hope this helps! Have a lovely day! :)

in the figure below, m || n. drag and drop each label into its corresponding box to show the appropriate angle pair

in the figure below, m || n. drag and drop each label into its corresponding box to show the appropriate

Answers

Answer/Step-by-step explanation:

A. <1 and <4 => vertical angles.

They share the same vertex/corner and are opposite each other as two straight lines intersect.

B. <3 and <5 => same-side interior angles.

They lie on the same side of the transversal and within the two parallel lines the transversal intercepts.

C. <4 and <5 => Alternate Interior Angles.

These angles lie on either side of the transversal, and within the parallel blinds cut across by the transversal.

D. <3 and <7 => Corresponding Angles.

They are found in the same side of the transversal occupying the same position.

what picture can you draw to show a thinking about 9÷4?

Answers

Think of

\(\frac{Green}{Red}\)

what picture can you draw to show a thinking about 94?

HI PLEASE HELP ON QUESTION ASAP USING AVERAGE (MEAN) TO ANSWER QUESTION! IF UR ANSWER AND EXPLAINATION IS CORRECT ILL RATE YOU FIVE STARS, A THANKS AND MAYBE EVEN BRAINLIEST. PLEASE MAKE SURE YOU ANSWER MY QUESTION USING AVERAGES.

1) a meal for 6 cost £12 per person. as it is one of the diners birthday , the other 5 decided to pay for his meal. how much do each of the five friends need to pay?

Answers

Each of the five friends needs to pay £14.40 to cover the cost of the birthday person's meal.

To calculate how much each of the five friends needs to pay, we can use the concept of averages or mean.

The total cost of the meal for 6 people is £12 per person. This means that the total cost of the meal is 6 * £12 = £72.

Since the other five friends have decided to pay for the birthday person's meal, they will evenly divide the total cost of £72 among themselves.

To find the average amount each friend needs to pay, we divide the total cost by the number of friends paying, which is 5:

£72 / 5 = £14.40

Using the concept of averaging or finding the mean allows us to distribute the cost equally among the friends, ensuring fairness in sharing the expenses.

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complete the partial two-way frequency table below that shows the extracurricular activities of high school students. Based on the data in the table, how many students do not play an instrument

Answers

According to the information, the missing number from the box is number 40.

How to find the missing number in the box?

To find the missing number of the table we must take into account different elements. In particular we must look at the totals and the columns and rows in which the empty space is. Once we identify the totals we can subtract the other values from the total and find the missing number in the table.

According to the above we can infer that the missing number is 40.

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complete the partial two-way frequency table below that shows the extracurricular activities of high
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