Given the lengths of two sides of a triangle, determine the range, a, of possible side lengths of the third side.

5 km and 11 km

12 mi and 12 mi

25 yd and 10 yd

Answers

Answer 1

By using the triangular inequality, we will get the possible lengths:

a) 6km < x < 16km

b) 0mi < x < 24mi

c) 15yd < x < 30yd

How to estimate the lengths of the possible third side?

If A, C, and D are the lengths of the sides of a triangle, then the triangular inequality says that:

A + C > D

A + D > C

C + D > a

Now, if the two sides are 5km and 11 km, and the other side is x, then we can write:

x + 5km > 11km

x + 11km > 5km

11 km + 5 km > x

From these inequalities we can get:

16km > x

x > 11km - 5km

x > 6km

Then the possible lengths of the third side are:

6km < x < 16km

b) Now the sides are 12 mi and 12mi, then the inequalities are:

x + 12mi  > 12mi

12mi + 12mi > x

The first one gives:

x > 0mi

The second:

24mi > x

The possible lenghts are 0mi < x < 24mi

c) 25 yd and 10 yd

Here we will get:

25yd + 10yd > x  ----- >  30yd > x

x + 10 yd > 25yd -------> x > 15yd

The possible lengths are:

15yd < x < 30yd

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Related Questions

y=3(x+2)^2+7 whats this equation

Answers

Answer:

See below

Step-by-step explanation:

This is a parabola in vertex form where the vertex is (-2,7) and the parabola is vertically compressed by a factor of 3.

REAL ANSWER PLEASE! CORRECT ANSWER TOO!

Answers

94 ounces

————————————

PLS HELP ME I ONLY HAVE 2 MINS TO ANSWER!!!!!!!!! ITS 100 PTS!!!!!

Three salesmen work for the same company, selling the same product. And, although they are all paid on a weekly basis, each salesman earns his paycheck differently. Salesman A works strictly on commission. He earns $65 per sale, with a maximum weekly commission of $1,300. Salesman B earns a weekly base salary of $300, plus a commission of $40 per sale. There are no limits on the amount of commission he can earn. Salesman C does not earn any commission. His weekly salary is $900. The following table shows the number of sales each salesman had during the first three weeks of this month.

Week 1 Week 2 Week 3
Salesman A 11 14 16
Salesman B 14 15 13
Salesman C 16 12 11

In which week(s), did Salesman C have a larger paycheck than both of the other salesmen? Select all that apply.

Week 3
None of the weeks.
Week 2
Week 1

Answers

In Week 1,

Salesman C got larger paycheck than Salesman A and Salesman B.

What is equation?

Mathematically, an equation can be defined as a statement that supports the equality of two expressions, which are connected by the equals sign “=”. For example, 2x – 5 = 13.

Here,

2x – 5 and 13 are expressions

The sign that connects these two expressions is “=”.

In algebra, an equation is a condition on a variable. It is satisfied only for a definite value of the variable. That means, the equation 2x – 5 = 13 is satisfied only for x = 9.

Given,

Commission of salesman A per sale = $65

Commission of salesman B per sale = $40

Commission of salesman C per sale = $0

Salary of salesman A per week = $0

Salary of salesman B per week = $300

Salary of salesman C per week = $900

No. of sales × commission + salary = total earning

In week 1.

Earning of A

11 × $65 + $0 = $715

Earning of B

14 × $40 + $300 = $860

Earning of C

16 ×$0 + $900 = $900

In week 2.

Earning of A

14 × $65 + $0 = $910

Earning of B

15 × $40 + $300 = $900

Earning of C

12 ×$0 + $900 = $900

In week 3.

Earning of A

16 × $65 + $0 = $1040

Earning of B

13 × $40 + $300 = $820

Earning of C

111 ×$0 + $900 = $900

By the above calculation Salesman C received $900 in week 1 which is greater than Salesman A and Salesman B.

In week 2 and week 3 his paycheck is smaller than both of the other salesman.

Hence, Salesman C  received larger paycheck than both of the other salesmen in Week 1.

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Sophia buys 11 bottles of pineapple juice at the corner store for a total cost of $9.90. Assume each bottle of juice is the same price. If c represents the total cost in dollars and cents of the juice for any number, j, of bottles of juice, write a proportional equation for c in terms of j that matches the context. How do I do that

Answers

The proportion equation for c in terms of j is written as c = 0.9j

How to write the equation

In order to find the proportional equation for c in terms of j that matches the context, what you would have to do would be to divide 9.90 dollars by 11 bottles of pineapple juice.

This would tell us the price that one of the bottles of juice is been sold for.

Hence we would have

9.90 / 11

= 0.9

Hence the equation would be: c = 0.9j

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Select the correct answer. what is the equation of a parabola whose vertex is (0, 5) and whose directrix is x = 2?
a. y2 = 8(x − 5)
b. 8(y − 5) = x2
c. (y − 5)2 = 8x
d. (y − 5)2 = -8x

Answers

Check the picture below, so the parabola looks more or less like so, with a vertex at (0 , 5) and a "p" distance of negative 2 units, since it's opening to the left, so

[tex]\textit{horizontal parabola vertex form with focus point distance} \\\\ 4p(x- h)=(y- k)^2 \qquad \begin{cases} \stackrel{vertex}{(h,k)}\qquad \stackrel{focus~point}{(h+p,k)}\qquad \stackrel{directrix}{x=h-p}\\\\ p=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix}\\\\ \stackrel{p~is~negative}{op ens~\supset}\qquad \stackrel{p~is~positive}{op ens~\subset} \end{cases} \\\\[-0.35em] ~\dotfill[/tex]

[tex]\begin{cases} h=0\\ k=5\\ p=-2 \end{cases}\implies 4(-2)(~~x-0~~) = (~~y-5~~)^2\implies {\Large \begin{array}{llll} -8x=(y-5)^2 \end{array}}[/tex]

The steps to solve an equation are shown below. Choose the reasons that are listed in the correct order to justify the steps in the solving process.

A- 1. Given, 2. Division Property of Equality, 3. Addition Property of Equality, 4. Division Property of Equality

B- 1. Given, 2. Multiplication Property of Equality, 3. Subtraction Property of Equality, 4. Division Property of Equality

C- 1. Given, 2. Division Property of Equality, 3. Addition Property of Equality, 4. Multiplication Property of Equality

D- 1. Given, 2. Multiplication Property of Equality, 3. Addition Property of Equality, 4. Division Property of Equality

Answers

The steps to solve the equation  (5y - 1)/2 = 7 are assigned and attached

D- 1. Given, 2. Multiplication Property of Equality, 3. Addition Property of Equality, 4. Division Property of Equality

How to solve the given equation

The expression in the problem is (5y - 1)/2 = 7

Clearing the fraction

The fraction is cleared by applying the Multiplication Property of Equality

(5y - 1)/2 = 7

5y - 1 = 14

Adding 1 to both sides of the equation is done using Addition Property of Equality

5y - 1 + 1 = 14 + 1

5y = 15

Making y the subject of formula Division Property of Equality is applied

5y / 5 = 15 / 5

y = 5

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We have x tables and y chairs available for prom.
If we put 12 chairs at each table there will be 4 extra chairs with no table.
If we put 14 chairs at each table, one whole table will be empty and another will only have 6 chairs.
How many available tables and chairs do we have available for the prom.

Answers

Answer:

looool

Step-by-step explanation:

Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-7,-6)
(6,3)
(4,-4)

Answers

The fourth point is (-6.5, -14)

Vertices of a parallelogram?

The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.

The three vertices you've provided are (-7,-6), (6,3), and (4,-4). To find the fourth vertex of a parallelogram, we can use the fact that opposite sides of a parallelogram are parallel and congruent, meaning they have the same length and the same slope.

One way to find the fourth vertex is to use the vector that connects one vertex to another. The vector from (-7,-6) to (6,3) is (13,9), and from (6,3) to (4,-4) is (-2,-7)

If we use the vector which is opposite of (-2,-7) that is (2,7) and add it to the third point (4,-4) , we will get the fourth point.

(2,7) + (4,-4) = (6,3)

so the fourth point is (6,3)

Another way is to find the midpoint of the diagonal of the parallelogram which are (-7,-6) and (4,-4) and then add the vector which is opposite of (6,3) to (4,-4) that is (-6,-9) which is also the vector from (6,3) to (4,-4)

Midpoint of (-7,-6) and (4,-4) = (-0.5,-5)

(-0.5,-5) + (-6,-9) = (-6.5, -14)

Hence, the fourth point is (-6.5, -14)

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Rewrite 14x4y3 − 42x3y4 using a common factor.

Answers

The expression 14x⁴y³ - 42x³y⁴ is rewritten to 14x³y³(x - y)

What is an algebraic expression?

An algebraic expression can be described as a mathematical expression that is made up of terms, coefficients, variables, factors and constants.

They are also made up of some arithmetic operations, such as;

SubtractionMultiplicationDivisionBracketParenthesesAddition, etc

From the information given, we have the algebraic expression;

14x⁴y³ - 42x³y⁴

Now, factor the common numbers, we have;

14(x⁴y³ - 3x³y⁴)

Factor the common variables, we get;

14x³y³(x - y)

Hence, the expression is 14x³y³(x - y)

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Plz help me with this no links

Answers

Answer:

11.7

Step-by-step explanation:

use the distance formula known as pythagorem theorem and plug in the x and y values.

What is the price per ounce of a 32‑ounce box of cereal priced at $4.16?

11 cents / ounce

12 cents / ounce


13 cents / ounce


14 cents / ounce

Answers

Answer:

13 cents / ounce

Step-by-step explanation:

$4.16÷32= $0.13 cents/ounce.

Complete the square
x^2+ 10x + 35

Answers

Answer:

sry i thought i knew how to do it but I can't remember

Step-by-step explanation:

Answer:

(x + 5)² + 10

Step-by-step explanation:

Given

x² + 10x + 35

To complete the square

add/ subtract ( half the coefficient of the x- term)² to x² + 10x

x² + 2(5)x + 25 - 25 + 35

= (x + 5)² + 10

Celia is 2 times Jacque’s age now. Celia was 6 times Jacque’s age 9 years ago. What system of equations can be solved to find their ages?
Group of answer choices

Answers

The answer is 78 I know this as I am smart

your uncle is 2 years older than your 3 times your age. a. you are x old. write an expression to describe your uncle's age. b. you are 12 years old. how old is your uncle

Answers

The age of your uncle is modeled by:

y = 2 + 3*x

Evaluating it, we can see that when you are 12 years old, your uncle will be 38 years old.

How to find the equation for your uncle's age?

Let's define the variables: y as your uncle's age and x as your age.

Here we know that your uncle is 2 years older than 3 times your age, so we can write the linear equation:

y = 2 + 3*x

This is the equation we needed to find.

b) If you are 12 years old, then we can write x = 12 in the equation above, then we will get:

y = 2 + 3*12

y = 2 + 36

y = 38

That's the age of your uncle.

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Suppose that 15 inches of wire costs 90 cents. At the same rate, how many inches of wire can be bought for 72 cents?

Answers

Answer:

12 inches

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

15 inches of wire costs 90 cents, then 1 inch of wire costs:

90/15 = 6 cents

The length of wire for 72 cents:

72/6 = 12 inches

What am I supposed to do?

Answers

its a virus dont  fall for it

Step-by-step explanation:

There are 30 students in an art class. Fourteen of the students are girls.
What is the ratio of boys to girls?

A.7:8
B.8 :7
C.8:15
D.14:40
E.30:14

Answers

Answer: B

Step-by-step explanation: To get the boys part of the ratio you will have to subtract 30 students and 14 students that are girls because all together there are 30 students and since we only know that 14 of them are girls that leaves the rest of the students boys. 30 - 14 = 16  so now we know how many boys there are. 16:14 can be reduced by 2 and that equals to 8:7.

Hope this helps!

The ratio of boys to girls is equal to: B. 8 :7

Given the following data:

Total students = 30 studentsNumber of girls = 14 students

To calculate the ratio of boys to girls:

How to calculate ratio.

First of all, we would determine the number of boys in the art class by subtracting the number of girl students from the total number of students in this class.

[tex]Total \;students = boys + girls\\\\30=boys + 14\\\\Boys =30-14[/tex]

Boys = 16 students.

For the ratio:

[tex]B:G=16:14[/tex]

Dividing by 2, we have:

[tex]B:G=8:7[/tex]

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Find the missing length of the right triangle.

Answers

Hopes this helps:

Answer: 65

Please mark as brainlist if it’s right.

Have a great day.


can someone please help me with these two questions I would really appreciate it they go together LINKS WILL GET REPORTED !

Answers

Here is your answer :

Answer 1 :

Volume of the Cylinder = πr²h

Therefore, The Volume of the Cylinder is 50.27 Feet

By Rounding, 50 Units/Feet

Answer 2 :

So, volume is always cubed since you have l x w x h.

A cubic ft is 12 in x 12 in x 12 in = 1728 in3.

35328.78/1728 = 20.44  

20.44 x 7.48 = 152.89

About 153 gallons

HOPE IT HELPS

Determine whether the graph of the given equations are parallel, perpendicular, or neither

Answers

Answer:

7) perpendicular

8) perpendicular

Step-by-step explanation:

If the equations are in the form:

y = mx + b

(they all are in this form in these questions)

the m, the number in front of the x, is the slope.

If the slopes are the "negative reciprocals" (opposite signs and flipped over from each other) of each other, then the lines are perpendicular.

You can also do a quick check by, if the m values are multiplied together you should get -1.

1/3 • - 3 = -1

1 • -1 = -1

1/3 and -3 have opposite signs and are reciprocals (flipped over)

1 and -1 are opposite signs. It isn't very obvious maybe that they are reciprocals, but they are. Like 1/1 flipped over is 1/1.

what 3 numbers multiplied equal 36

Answers

Answer: 3 times 4 times 3

Step-by-step explanation:

Answer:

6 x 3 x 2 = 36

Step-by-step explanation:


Is it possible for two lines with negative slopes to be perpendicular? Justify your answer.

Answers

Answer:

No

Step-by-step explanation:

The slopes of perpendicular lines must always be the negative reciprocal of each other. If one slope is negative, for the other to be perpendicular to it, it must be positive, and vise versa.

Answer:

No

Step-by-step explanation:

Interesting question. Subtle.

The formula for two lines to be perpendicular is m1 * m1 = -1 That means that two lines cannot be minus -- only 1 of them can be. The reason is that if both were minus when multiplied together would give a positive result -- not minus one. For example, suppose you have

y = x + 2  

y = 2x + 3.

These 2 lines will cross and they are not parallel, but neither are they perpendicular. I'm not going to solve this to find out where they cross -- that's not what you are asking.

Now suppose you have two other lines

y = - 2x + 3

y = 1/2 x + 1

These two lines should be perpendicular

-2 * 1/2 =  - 1 which is the condition of perpendicular.

Separate graphs have been uploaded to help you understand.

{what is the area of the shaded region of the parallelogram below?}
plshelp!!

Answers

Answer:

J)  924 cm²

Step-by-step explanation:

the shaded area represents a trapezoid and the formula for area is:

1/2 x height x (sum of parallel bases)

A = 1/2(24)(35+42)

A = 12(77)

A = 924

What are the actual dimensions of the Books section?

Answers

Answer:

b.

Step-by-step explanation:

50PTS 50 PTS (DONT explain just answer please)

Answers

Answer: 17

Step-by-step explanation:

Answer:

x = 17°

Step-by-step explanation:

The given angles are,

→ 6x + 8

→ 4x + 2

Now we have to,

→ find the required value of x.

Forming the equation,

→ (6x + 8) + (4x + 2) = 180°

{As two angles in a straight line is 180°}

Then the value of x will be,

→ (6x + 8) + (4x + 2) = 180°

→ 6x + 4x + 8 + 2 = 180°

→ 10x + 10 = 180°

→ 10x = 180° - 10

→ x = 170/10

→ [ x = 17° ]

Hence, the value of x is 17°.

Trey and three of his friends are ordering a pizza. They plan to split the cost, and the want to spend at most $3.50 per person. Write and solve an inequality to find the cost of the pizza they should order.​

Answers

The inequality to find the cost of the pizza they should order is c ≤ 14. The cost is at most $14.

How to express the inequality?

Inequalities are simply created through the connection of two expressions. In this case, it should be noted that the expressions in an inequality are not always equal. Inequalities implies that the expressions are not equal. Here, they are denoted by the symbols ≥ < > ≤.

Since Trey and three of his friends are ordering a pizza and they want to spend at most $3.50 per person. An inequality to find the cost of the pizza they can order is:

c ≤ (3.50 × 4)

c ≤ 14

The cost will be at most $14.

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How do you know if 3 lengths will make a triangle?

Answers

If three lengths can make a triangle by using the Triangle Inequality Theorem which states . that any two triangle sides added together must exceed the third side If the sum of any two sides is equal to or less than the third side, then the lengths cannot make a triangle.

The Triangle Inequality Theorem can be used to determine if a triangle can be formed from three lengths. According to this theorem, any two triangle sides must add up to more than the third side. To put it to use, add up the lengths of the first two sides and compare them to the third side's length. The lengths cannot form a triangle if the total of the first two sides is more than or equal to the third side. The lengths can form a triangle if the product of the first two sides is bigger than the product of the third side.

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Data on the fuel consumption y of a car at various speeds x is given. Fuel consumption is measured in mpg, and speed is measured in miles per hour. Software tells us that the equation of the least‑squares regression line is ^ y = 55. 3286 − 0. 02286 x

Answers

Fuel consumption is 53.957 miles per gallon for a car moving at  a speed of 60 miles per hour using least square Regression .

What is Regression ?

A statistical word for models that evaluate the connections between variables is regression. A single dependent variable Y and one or more independent variables X are studied using a linear regression model.

A technique for employing a goodness-of-fit criterion to fit a curve—not necessarily a straight line—through a collection of points. Regression that is most frequently used is linear regression. Recursion is occasionally used interchangeably with the word regression.

Y = mX + b, where X is the predictor (independent) variable, m is the estimated slope, and b is the expected intercept, is the formula for simple linear regression.

Calculation of Fuel Consumption in 60 miles per hour.

given the least square regression line is

y = 55.3286 - 0.02286x

so, y = 55.3286 - 0.02286 * 60 = 53.957 miles per gallon.

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Sarah has £135
gemma has £70
beth has £35

sarah gives some of money to gemma and beth.

the ratio of the amount of moneu sarah, gemma and beth have now is 3:2:1.

How much money did sarah give to gemma???

pls help i so stuck and i need the answer quick!

Answers

Answer:

£10 pounds

Step-by-step explanation:

135+70+35 = 240 pounds between all 3

3:2:1 ratio means 6x represents all of them

6x=240

x=£40 each 1

3(40) =  £120 Sarah

2(40) = £80  Gemma

1(40+ = £40  Beth

Gemma received 10 pounds.

Hay can some one help me I need the answers

Answers

Answer:

check: 2,3,5,8

Step-by-step explanation:

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