Two sides of a triangle are
shown. Find the range of
values of the third side.
10, 5
< X
Answers
Answer:
5 < x < 15
Step-by-step explanation:
The triangle inequality theorem states that the sum of the measures of any two sides of a triangle must be greater than the measure of the third side
In the given triangle we are provided measures of two of the sides as 10 and 5
Let the measure of the third side be x
So the three sides are 10, 5 and x
Then by the inequality theorem
10 + 5 > x
==> 15 > x or
x < 15 This is an upper bound for x
when we switch sides in an inequality > changes to < and < changes to >
We also have
x + 5 > 10 ==> x > 10 - 5 ==> x > 5
and
x + 10 > 5 ==> x > -5
Since x > 5 is more restrictive than x > -5, we conclude that x > 5 or 5 < x is the lower bound on x
Combining all inequalities we get
5 < x < 15
Note
We could also state the lower and upper bound limits as
difference of two sides < x < sum of two sides
10 - 5 < x < 10 + 5
or
5 < x < 15
While this may seem easier to compute than the explanation given above, the derivation is left out and may confuse some students
Related Questions
3x-1=5x+10x= 5 1/2
please explain to me what did i do wrong and correct it
Answers
The requried correct expression 3x - 1 + 5x + 10x = 5 1/2, and solution of the equation is x = 7.5/18
What are equation models?The equation model is defined as the model of the given situation in the form of an equation using variables and constants.
The equation as written doesn't have a unique solution, as the left-hand side and right-hand side are not equal.
To correct the equation, you would need to provide more information about what you intended to do with the two equations and format the right-hand side of the equation properly. For example, if you meant to add the two equations, you could write,
3x - 1 + 5x + 10x = 5 + 2.5
18x = 7.5
x = 7.5/18
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Multiply left-parenthesis x plus 2 right-parenthesis left-parenthesis x minus 6 right-parenthesis
Answer options
A.
x squared minus 8 x minus 12
B.
x squared plus 8 x minus 12
C.
x squared minus 4 x minus 12
D.
x squared plus 4 x minus 12
E.
x squared minus 4 x plus 12
Answers
Answer:
[tex]x^{2}-4x-12[/tex]
Step-by-step explanation:
(x+2)(x-6)
STEP 1 - USE FOIL
(FOIL is a standard way of multiplying 2 fractions, just multiply in the following order):
Forward
Outside
Inside
Last
(x+2)(x-6) becomes this when you FOIL it:
[tex](x^{2} )(-6x)(2x)(-12)[/tex]
STEP 2 - COMBINE ALL THE TERMS
[tex]x^{2}[/tex] has to stay by itself because there are no other squares. [tex]-6x+2x=-4x[/tex] because you're adding two to -6 which effectively is 6 - 2 but you're adding a negative sign. And [tex]-12[/tex] stays the same because there are no x's in it.
STEP 3 - WRITE THE SOLUTION
All in all, the final solution, once you put everything together, is:
[tex]x^{2} -4x-12[/tex]
Pre cal due tonight pls help
Answers
The dot product a . b is -22
What is the dot productThe dot product, also known as scalar product or inner product, is a binary operation that takes two vectors and returns a scalar (single-valued) quantity. The dot product of two vectors is equal to the product of the magnitude (length) of the vectors and the cosine of the angle between them.
Given two vectors, A and B, the dot product is defined as:
A ∙ B = |A| * |B| * cos(θ)
where |A| and |B| are the magnitudes of vectors A and B, and θ is the angle between them.
a = <3, -2>
b = <-2, 8>
a . b = (3 * -2) + (-2 * 8)
a . b = -6 + - 16
a . b = -22
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At the start of a party, a drink dispenser contains 912 quarts of iced tea. After the party only 7 cups of tea remain. How many cups of iced tea did people drink during the party?
Answers
Amount of iced-tea consumed during party was 92 cups, which is equivalent to 23 quarts. It's important to note difference between volume units such as cups and quarts, and the conversion factor between them.
To determine the number of cups of iced-tea that were consumed during the party, we need to subtract the amount that remained from the total amount that was in the drink dispenser at the start of the party.
One cup of iced tea is equal to 1/16 of a quart, so 7 cups is equal to
7 * (1/16) = 7/16 quarts.
Thus, the total amount of iced tea that was consumed during the party is 912 quarts -
7/16 quarts = 912 - 7/16
= 912 - 7 * (1/16)
= (912 * 16 - 7 * 1) / 16
= 1476 / 16
= 92.25 cups, rounded down to the nearest whole number, which is 92 cups.
It is important to note that the answer is given in cups and not quarts. Quarts is a unit of volume and cups is a unit of volume as well, but they are not equivalent. 1 quart is equal to 4 cups. If we wanted to express the amount of iced tea consumed in quarts, we would multiply the answer by 1/4.
In conclusion, the number of cups of iced tea consumed during the party is 92 cups, and if we express this in quarts it is equivalent to
92 * (1/4) = 23 quarts.
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Solve for x.
X
A
=
2
C
1
B
1
E
X
D
Answers
Step-by-step explanation:
ABC and ADE are similar triangles.
that means they have the same angles, and there is one scaling factor for all sides from one triangle to the other.
so, we see that AB = 2, AD = 2+1 = 3
the scaling factor f from AB to AD is then
AB × f = AD
2 × f = 3
f = 3/2
the same scaling factor now applies between BC and DE (= x).
BC × f = x
1 × 3/2 = x
x = 3/2 = 1.5
the bakery made $600 Donuts they made 384 more Donuts than Bagels the bakery made 216 Bagels
Answers
The bakery made 384 donuts and 216 bagels
What is bakery?
A bakery is a business that produces and sells baked goods, such as bread, cakes, pastries, and cookies.
Let's use the variable "x" to represent the number of bagels made.
From the problem, we know that:
The number of donuts made is 384 more than the number of bagels made, so the number of donuts is x + 384.
The bakery made 216 bagels.
We also know that the bakery made a total of 600 donuts. So, we can set up an equation to represent the total number of pastries made:
x + 384 + 216 = 600
Simplifying and solving for x:
x + 600 = 600
x = 600 - 600 + 384
x = 384
So, the bakery made 384 + 216 = 600 pastries in total.
Therefore, the bakery made 384 donuts and 216 bagels.
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What is the end behavior of f(x)?
f(x) = -252x+6x³ +30x² - 864
as x→→∞, f(x) → ∞ and as x→∞, f(x) →∞
as x-x, f(x) → ∞ and as a →∞, f(x) →→∞
as x-x, f(x) → ∞ and as a →x, f(x) →∞
as x→→∞, f(x) →→∞ and as x →∞, ƒ(x) →→∞
Answers
Answer: 27
Step-by-step explanation:
select the number that comes next in the sequence of numbers below 6 12 20 26 34 40
Answers
GIVE BRAINLIEST PLEASE!
thank you and have a good day :)
Answer:
48
Step-by-step explanation:
the sequence of numbers alternates between adding 6 and 8.
6 + 6 = 12
12 + 8 = 20
20 + 6 = 26
26 + 8 = 34
34 + 6 = 40
40 + 8 = 48!
i hope this helps :)
Answer:48
Step-by-step explanation:The sequence adds 6 first then adds 8
A travel club can spend at most 10 nights in two cities on a trip. The club needs to reserve four rooms each night and wants to spend no more than 4200 on hotels and fuel. The estimated fuel cost is 200 can the club spend 3 nights in city a and 6 nights in city b? 7 nights in city a and 3 nights in city b? justify your answer using a system of linear equations
Answers
To solve this system, we must first determine the number of available rooms in each city, as well as the per-night cost of hotel rooms. Without that information, we can't tell if the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B.
Let's start by defining the variables we'll need to solve this problem:
Assume that x is the number of nights spent in City A.
Let y represent the number of nights in City B.
To determine whether the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B, we must first determine whether the total cost of hotels and fuel for each scenario is less than or equal to $4200.
Given that the estimated cost of fuel is $200, the cost of hotels must be less than or equal to $4000.
The following equations calculate the cost of hotels for each scenario:
3x + 6y = cost of hotels for spending 3 nights in city A and 6 nights in city B7x + 3y = cost of hotels for spending 7 nights in city A and 3 nights in city BWe also know that the club can only spend a total of 10 nights, so x + y must be less than or equal to 10.
Finally, we must ensure that the club can book four rooms each night. This means that the number of rooms required per night in each city is four times the number of nights. As a result, we must have:
4x ≤ number of available rooms in city A4y ≤ number of available rooms in city BWhen we combine all of these constraints, we get the following system of linear equations:
3x + 6y + 200 ≤ 4200 (cost constraint for spending 3 nights in city A and 6 nights in city B)
7x + 3y + 200 ≤ 4200 (cost constraint for spending 7 nights in city A and 3 nights in city B)
x + y ≤ 10 (total number of nights constraint) (total number of nights constraint)
A city with 4x available rooms (room constraint for city A)
4y rooms available in city B (room constraint for city B)
To solve this system, we must first determine the number of available rooms in each city as well as the cost of hotel rooms per night. We can't tell if the club can spend three nights in city A and six nights in city B, or seven nights in city A and three nights in city B, without that information.
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please help meeeeh:
Find the first four terms and stated term given the arithmetic sequence, with a, as the 1" term.
an = 25 - 10n, a5
an = 11 + 9n, a6
an = 65 - 35n, a9
Answers
Answer:
The nth term of an arithmetic sequence is given by an = a + (n – 1)d ... Step 1: First, calculate the difference between each pair of adjacent terms.
Step-by-step explanation:
Hope this help's you
name the ray that is opposite FH.
Answers
Answer: Ray HF is opposite of Ray FH
Step-by-step explanation:
E(t)E, left parenthesis, t, right parenthesis models the daily amount of energy (in kilojoules, \text{kJ}kJstart text, k, J, end text) that a solar panel in Pago Pago generates, ttt days after the autumn equinox. Here, ttt is entered in radians. E(t) = {624}\sin\left({\dfrac{2\pi}{365}}t\right) + {8736}E(t)=624sin( 365 2π t)+8736E, left parenthesis, t, right parenthesis, equals, 624, sine, left parenthesis, start fraction, 2, pi, divided by, 365, end fraction, t, right parenthesis, plus, 8736 What is the first day after the autumn equinox that the solar panel generates 8400\text{ kJ}8400 kJ8400, start text, space, k, J, end text?
Answers
The first day after the autumn equinox that the solar panel generates 8400 kJ is approximately 39.2 days, or 0.107 radians, after the equinox.
To find the first day after the autumn equinox that the solar panel generates 8400 kJ, we need to solve the equation:
624sin(2π/365)t + 8736 = 8400
Simplifying the equation, we get:
sin(2π/365)t = 0.958
Taking the inverse sine of both sides, we get:
(2π/365)t = 1.296 or (2π/365)t = 3.846
Solving for t in each equation, we get:
t ≈ 78.97 or t ≈ 235.62
Since t is measured in radians, we need to convert it to days by dividing by 2π/365:
t ≈ 78.97 / (2π/365) ≈ 86.75 or t ≈ 235.62 / (2π/365) ≈ 256.73
Therefore, the first day after the autumn equinox that the solar panel generates 8400 kJ is either day 87 or day 257.
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Find the values of x and y.
Answers
7y=168
Y=24
2y+12+5x=90
48+12+5x=90
50+5x=90
5x=40
X=8
Hope this helps!
In my own words, write the 4 steps in finding the unknown angle of the givin right triangle
Answers
Answer:
Step-by-step explanation:
This question of of Trigonometry
Tan means the ratio of sides which are opposite to the given angle divided by the adjacent side to the angle (NOT THE HYPOTENUSE)
So Tan(Unknown angle) = 5/14
Unknown angle = 19.6 Degrees
4 Write an expression
explaining the depth of
an Olympic pool that
goes to 50 ft. deep.
Answers
The depth of an Olympic pool that goes to 50 ft. deep can be expressed as:
d = 50 ft.
What is olympic pool?
Olympic pool is a type of swimming pool that is used for competitive swimming and diving events. These pools typically have a uniform depth, a smooth and flat bottom and multiple lanes for swimmers to compete in.
The depth of an Olympic pool that goes to 50 ft. deep can be expressed as:
d = 50 ft.
Where d is the depth of the pool. This expression simply states that the depth of the pool is equal to 50 ft.
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which number below is most unlike the others ?? 102, 203, 506, 608
Answers
Sanjay made cookies for a bake sale and has tracked his sales by cookie shape. cat 36 star 14 dog 35 Considering this data, how many of the next 51 cookies sold should you expect to be in the shape of a dog?
Answers
The number of cookies sold that would be in the shape of the dog in the next 51 cookies is 21.
What is probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means. You will understand the potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution. Knowing the total number of outcomes is necessary before we can calculate the likelihood that a specific event will occur.
The probability of cookies sold in shape of dog is:
P = 35/85
The number of cookies sold that would be in the shape of the dog in the next 51 cookies is:
N = 51 (P)
N = 51 (35/85)
N = 21
Hence, the number of cookies sold that would be in the shape of the dog in the next 51 cookies is 21.
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Look at the image below.
Answers
Answer: 28 (look at the image for the solution)
Step-by-step explanation:
Answer:
A = base x height
A = 7 x 4
A = 28
Have a wonderful day! :-)
Part Two Using the diagram above, answer the following questions. Answer both parts of each question. For questions 7 and 8, identify the process as either cellular respiration, photosynthesis or both. True or False. The arrow labeled C represents a transfer of chemical energy to mechanical energy. Explain why this is true or false. True or False. The arrow labeled A represents a transfer of solar energy to chemical energy. Explain why this is true or false. Which arrow or arrows represent a release of carbon dioxide? What process is occurring at the arrow(s) you selected? Which arrow or arrows indicate a process that cycles carbon from living or nonliving organisms? Describe the process or processes you selected. Which arrow or arrows represent reactions that demonstrate a conservation of mass and energy? Explain your answer.
Answers
The arrow labeled C represents a transfer of chemical energy to mechanical energy. False, this is because, the gas released does not do any work.
The arrow labeled A represents a transfer of solar energy to chemical energy. True, chemical energy is stored in starch molecules
The arrows that represent the release of carbon dioxide is C. This is combustion and it occurs in nonliving things. The process involves the burning of carbon materials.
The conservation energy is demonstrated by arrow A since we can show it by a chemical reaction.
What is the carbon cycle?
The carbon cycle is the process by which carbon atoms circulate through the Earth's atmosphere, oceans, and landmasses. In the carbon cycle, carbon is exchanged between the atmosphere, biosphere, hydrosphere, and geosphere. The main components of the carbon cycle include photosynthesis, cellular respiration, decomposition, and combustion.
In photosynthesis, plants take in carbon dioxide from the atmosphere and convert it into organic compounds, which serve as food for the plants and are stored in their tissues.
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Can someone explain this
Answers
Step-by-step explanation:
This is a family of curves represented by the equation:
y = a (x + 4) (x − 2)
Different values of the a coefficient result in different quadratic functions.
The vertex of the parabolas is halfway between the zeros, at x = -1.
y = a (-1 + 4) (-1 − 2)
y = -9a
So to find the value of a, divide the y-coordinate of the vertex by -9. For example, curve A has a vertex at (-1, -3), so the value of the a coefficient is -3 / -9 = ⅓.
A. y = ⅓ (x + 4) (x − 2)
B. y = (x + 4) (x − 2)
C. y = 2 (x + 4) (x − 2)
D. y = -⅓ (x + 4) (x − 2)
E. y = -2 (x + 4) (x − 2)
ANSWER QUICK!! I WILL GIVE BRAINLIEST!!!!!!!!!!!
The barber cuts 61 haircuts in 4 days. Determine the rate for a ratio of the two different quantities.
61 over 65 haircuts per day
4 over 65 haircuts per day
4 over 61 haircuts per day
61 over 4 haircuts per day
Answers
Answer:
61 over 4 haircuts per day
What is a ratio?
A ratio has two or more numbers that symbolize relation to each other. Ratios are used to compare numbers, and you can compare them using division.
A way to solve for the number of haircuts per day is to use this equation:
total number of haircuts ÷ number of days = haircuts per dayYou could also use this fraction:
[tex]\frac{total-number-of-haircuts}{number-of-days}[/tex]Inserting the numbers into the fraction::
[tex]\frac{61}{4}[/tex]Therefore, the rate for a ratio using the two different quantities is 61 over 4 haircuts per day.
Beth added 1 1/4
pounds of fruit to a fruit basket. Her son took 2 3/8 pounds
of fruit out of the basket. What was the total change in pounds of fruit in the
fruit basket?
Answers
Answer: To find the total change in pounds of fruit in the basket, we need to subtract the amount taken out from the amount added.
First, let's convert all the fractions to decimals:
1 1/4 = 1.25
2 3/8 = 2.375
Now, we can subtract:
1.25 - 2.375 = -1.125
So, the total change in the fruit basket was -1.125 pounds, meaning the basket had 1.125 pounds less fruit after the removal.
Step-by-step explanation:
Fill in the missing term and select the
missing description. Simplify any fractions.
6(a + 2)
a + 2 =3
a =
Subtract 2 from both side
Answers
The value of a in the equation a + 2 = 3 is 1.
How to calculate the valueAn equation simply has to do with the statement that illustrates the variables given. In this case, it is vital to note that two or more components are considered in order to be able to describe the scenario.
It is important to note that an equation is the mathematical statement which can be made up of two expressions which are connected by an equal sign.
a + 2 = 3
Subtract 2 from both sides
a + 2 - 2 = 3 - 2
a = 1
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State if the lines are Parallel, Perpendicular, or Neither. 4x+y=5 3x+12y=-6
Answers
The lines 4x+y=5 and 3x+12y=-6are neither parallel nor perpendicular
How to determine the relationship between the linesFrom the question, we have the following parameters that can be used in our computation:
4x+y=5 3x+12y=-6
Make y the subject in the equations
So, we have
y = -4x + 5
y = -1/4x - 1/2
The slopes of the lines are -4 and -1/4
These numbers are not equal and they are not opposite reciprocals
This means that the lines are neither parallel nor perpendicular
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A little boy accidentally let go of his ballioon, and it floated away. It was 2 meters above the
ground when he let go, and it steadily rose 1 meter per second.
Write an equation that shows the relationship between the number of seconds since the boy
let the balloon go, x, and its elevation in meters, y.
y=
Answers
Answer:
Step-by-step explanation:
y=2+x
1m per second.
2+1x=2+x=y
find the relational column formula.
What algebraic expression could represent the average of 2x, 3 + x and 6x?
Answers
The algebraic expression in simplified form representing the average is 3x + 1.
To solve this question, one must know the formula of average. It is as follows -
Average = sum of the numbers / quantity of numbers
Now, we see that there are 3 expressions in the question. Hence, quantity of numbers will be 3.
Sum of the numbers = 2x + 3 + x + 6x
So, keep the values in formula to find the expression -
Average = 2x + 3 + x + 6x/ 3
Simplifying the expression to find average
Average = 9x + 3/3
Performing division on Right Hand Side of the equation
Average = 3x + 1.
Hence, required algebraic expression is 3x + 1.
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please help i will mark as brainliest i promise
Answers
The triangles ΔGFN and ΔJFN are congruent to each other by the SAS postulate. Then ∠FGN = ∠FJN.
What is the triangle?The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180°.
The line segment GF = NJ and FN bisect the angle ∠GFJ.
In triangles ΔGFN and ΔJFN, then we have
GF = NJ (Given)
∠GFN = ∠JFN (Given)
NF = NF (Common sides)
The triangles ΔGFN and ΔJFN are congruent to each other by the SAS postulate. Then we have
∠FGN = ∠FJN
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a gambler has a fair coin and a two-headed coin in his pocket. he selects one of the coins at random; when he flips it, it shows heads. what is the probability that it is the fair coin?
Answers
The probability of selecting the fair coin when a gambler has both a fair coin and a two-headed coin in his pocket is 50%.
This is because, when he selects one of the coins at random, it is equally likely that he has chosen either the fair coin or the two-headed coin. If he flips the coin and it shows heads, then the probability that it is the fair coin is still 50%, because either coin could have been selected and both would show heads.This is an example of a classical probability problem, which is based on the law of equal chances. This law states that when an event has multiple possible outcomes, each of those outcomes is equally likely to occur. In this case, there are two possible coins that could have been chosen, so each coin has a 50% chance of being selected. This means that the probability of selecting the fair coin is 50%.This also applies to events that have multiple outcomes which are not equally likely. For example, if a gambler has a fair coin, a two-headed coin, and a three-headed coin in his pocket, the probability of selecting the fair coin is still 50%. This is because the gambler has an equal chance of selecting any of the coins, regardless.
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It says its wrong is it?
Answers
Answer: Yes, it's wrong.
Step-by-step explanation:
In the equation, it was [tex]A=\pi r^{2}[/tex]3 ft is the circle's diameter, and d is not the r.
r = d/2 = 3/2 = 1.5 ft
[tex]A=\pi r^{2}\\[/tex]
≈ 3.14 x 1.5
= 4.71
+Ready
Practice Write and Solve Mulo-Step Equations-Quid-Level
Three sides of a quadrilateral are the same length, q. The length of the fourth side is 7 inches.
The perimeter of the quadrilateral is 40 inches.
Write an equation that represents
the situation.
+
9
3
7
40
11
7
9
9
Answers
The equation that represents the situation is q = 40 - 7
How to determine the perimeterThe formula for the perimeter of a quadrilateral is expressed as;
P = a + b + c + d
Where the sides, a , b , c and d are all the sides of the quadrilateral
From the information given, we have that;
The sides are a, the fourth is 7
The perimeter = 40 inches
Substitute the values
40 = 7 + q
collect the like terms, we get
q = 40 - 7
subtract the values
q = 33 inches
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